They named her Amazing Grace for good reason. In the aquamarine waters of Laguna San Ignacio off Mexico's west coast, this bold grey whale sidled up to the research vessel and began pushing the boat along like a rubber duck.

The female behemoth, with a distinctive long scar on her nose, "was the first friendly whale we ever experienced", says researcher Steven Swartz.

For obvious reaons, whales had learned to fear humans

It was 1977, and Swartz had arrived in Baja Mexico months earlier to study the lives of these wintering grey whales. "It bumped and raised our boat, pushing us from side to side." Gracie even allowed the researchers to pet her.

At that time, a whale getting friendly with humans "was a very rare event", Swartz explains. For obvious reasons, whales had learned to fear humans – whaling boats had been common for decades. Gracie was the exception to the rule.

But by 1982, friendly whale encounters had become more common and they remain so today. Now, Swartz estimates that at any one time, about 80-90% of the whales he studies are not in the least bothered by boats – and a few are comfortable enough to come up and explore or even follow boats around. "Sometimes they don't come close," he says, "but they'll just be right behind you all the time."

As whalers have largely given way to whale-watching tourists, the fear some whales once associated with humans seems to have been replaced by curiosity. But as we learn more about whales and dolphins, some researchers have begun asking a new question: is whale-watching really as benign as it seems?

The Amazing Grace experience may have been the first "friendly" whale encounter in Laguna San Ignacio documented by a scientist, but the locals had experienced similar interactions before. Known locally as "the chosen one", fisherman Don Pachico Mayoral had his own story of a friendly whale encounter.

Reaching out, the fisherman nervously touched it with his hand

In the winter of 1972, Pachico and a partner had been fishing from their 18-foot (5.5m) wooden panga when a grey whale twice the size of their boat approached. Fearing for their lives, the two fishermen tried to get away.

Pachico had good reason to be concerned. Over centuries of whaling, grey whales had earned the nickname of "devilfish" for their habit of fighting back against the whalers. Sometimes the whalers were the ones that got killed.

Each time Pachico changed the boat's direction, the whale would follow: the two men prepared for the worst. But then something surprising happened. Rubbing itself gently against the panga, the grey beast raised its head out of the water right beside Pachico.

Reaching out, the fisherman nervously touched it with his hand. To his surprise, the whale didn't back away. It moved even closer, as if to encourage the intimacy. It was an experience that was to change local attitudes towards whales forever.

"Unfortunately we lost Pachico a few years ago but his family is still there, running an ecotourism business," says Swartz. Theirs is one of many whale-watching businesses in the region. Now the wintering grey whales are hunted by cameras, not harpoons.

Grey whales had earned the nickname of "devilfish" for their habit of fighting back against the whalers

In the 80 years since the first moves to protect whales from commercial whaling, these devilfish are losing their bad reputation.

But it is up for debate whether the whales would agree that humans, too, have lost their bad reputation.

For instance, when whale watching first began in Baja Mexico in the 1970s, "there were no guidelines", explains Swartz. That meant whales were sometimes chased and harassed by high-speed boats packed with tourists.

Today, whale watching in Laguna San Ignacio is closely regulated. This whale habitat is part of a United Nations World Heritage Site and Mexico's El Vizcaino Biosphere Reserve.

A whale sheriff carefully monitors traffic in the lagoon, making sure there are not too many boats present at any one time. They must also stay within specific zones, observe 90-minute time limits, and not purposely approach the whales. The region is an example of well-regulated whale tourism.

However, there are still plenty of places around the world where marine mammal watching is regulated poorly – or not at all.

The impacts of marine wildlife tourism on the creatures being watched has long intrigued David Lusseau. As a teenager learning to dive on the French coast of the Mediterranean, Lusseau was intrigued by one lone dolphin that would spend time with the divers.

Boats seem to be perceived in the same way across many species: as a risk

"That individual seemed to change his behaviour a lot depending on how people behaved around it." When the dolphin came into the bay, people would rush to the water to try to touch it and jump on it. "It just seemed wrong," he says, "because the animal would become quite distressed, and tried to get away."

In many cases it had to fight its way out.

Yet around divers further out to sea, the same dolphin was calm and curious. "He would actually follow you underwater," Lusseau recalls. That observation, he says, "tickled my interest".

Lusseau's fascination with dolphin behaviour stuck with him. His doctoral work involved studying the effects of tourism on the critically endangered population of bottlenose dolphins in Fiordland, New Zealand. Continuing his work at the University of Aberdeen in Scotland, he has recently looked at how a range of marine mammals, including both whales and dolphins, behave in the presence of wildlife-watching boats.

He and colleagues have found that boats seem to be perceived in the same way across many species: as a risk.

There is plenty of evidence that whales and dolphins respond to boats as they would to a predator.

Many cetaceans – whales, dolphins and porpoises – spend more time underwater in the presence of boats. Lusseau's work on bottlenose dolphins in Doubtful Sound, New Zealand, revealed that these animals sometimes react to boats even before they can see them.

They abandon the fjord where tourism exposure occurs

In places where the number of whale-watching boats is small, and whales range over large distances, the effects of whale watching can be small.

Lusseau and colleagues studied this in minke whales in Faxafloi Bay, Iceland, where whale exposure to whale watching is relatively low. Here at least, whale watching appears to have insignificant effects on their feeding and other activities, which is good news for the long-term survival of the whale population.

But for the dolphins of Fiordland, New Zealand, the same cannot be said.

Once the level of tourism is high, "they abandon the fjord where tourism exposure occurs", says Lusseau.

Swimming alongside boats can save them energy – like slipstreaming

His work suggests that where these animals cannot avoid high levels of tourism, it takes a toll on their babies. Lusseau has found that as tourism volume increases, dolphin feeding efficiency declines, reducing their energy intake.

"The energy they would divert into making milk seems to be reabsorbed into maintaining survival probability for the female," he explains. In these high-tourism conditions, "we see the survival probability over the first year of life of a calf drop from around 86% to around 38%, which is a huge impact", he says.

These animals are long-lived, slow-reproducing species, says Lusseau, which means that theoretically at least, it is cheaper over their lifespan to avoid risk when possible. But some individuals clearly do take risks. Why do certain individuals approach boats?

We do not know for sure why Amazing Grace and her friends do so. But as far as smaller animals like dolphins and porpoises are concerned, swimming alongside boats can save them energy – like slipstreaming.

Even the skipper on the top deck of the 50-passenger boat could feel the vibration

Hitching a ride is a means to reduce the cost of transport on long voyages, Lusseau explains. "What we see a lot is teenagers doing what teenagers do in all long-lived species: they take risks," he says. It is often the youngsters that bow-ride and zigzag in front of boats, he has discovered.

Rarely, dolphins even ram boats. That is something Lusseau has observed only once, 13 years ago.

The day after a New Zealand tour boat ran over and killed an adult male dolphin with its propellers, two of the dead male's associates "swam as fast as I've ever seen an animal swim in the water without porpoising, and just rammed the boat".

Even the skipper on the top deck of the 50-passenger boat could feel the vibration, while Lusseau observed the whole thing from his own research vessel.

Putu Mustika, an adjunct researcher at James Cook University in Australia, and co-founder of the non-profit Cetacean Sirenia Indonesia, has also been exploring how dolphins react to being closely watched by humans in boats. It is a research area she was alerted to by journalists concerned by the practice of boats chasing dolphins.

Often these speedy tour boats herd and divide up social groups of dolphins, like marine sheepdogs

For the spinner dolphins she studies in Lovina, North Bali, there is, as yet, no formal protocol for marine mammal watching. As a result, it is not uncommon for there to be more dolphin-watching boats than dolphins.

"In peak season, there might be 80 boats around the dolphin, and other times, 30 to 40," she says.

So while those on boats watched the dolphins, Mustika watched the boats, recording human behaviour as well as the response of the dolphins. She also surveyed the attitudes of the boat operators, who claimed, anecdotally, that the number of dolphins in the region has declined since dolphin tourism began.

Often these speedy tour boats herd and divide up social groups of dolphins, like marine sheepdogs. Yet tourist satisfaction, she found in her surveys, was highly influenced by boat speed.

Peak resting time is 10:00 to 14:00, making it "peak human time" too

"Of course they want to see a lot of dolphins, but what is more important is that they see them without them being harassed," says Mustika, explaining that many of these tourists are highly educated Westerners, who find wildlife harassment repugnant.

As yet, her research has not translated into guidelines, though many of the tour boat operators have agreed to keep their distance and reduce their speed. There is an emerging understanding that without respect for the dolphins, "you won't be able to see them anymore", she explains.

Most of the tourism operators are fishers by trade, but 40% of their income comes from this sideline business. That means that if the dolphins disappear, so too does this source of income.

Tourism experience versus dolphin well-being is also a problem off the beautiful beaches of Hawaii, where Heather Heenehan is studying the tricky conflict between humans and spinner dolphins for her doctoral research at Duke University.

The Hawaiian spinner dolphin, so named because of its unusual aerial acrobatics, feeds offshore at night, hunting for fish, shrimp, and squid. Working together in groups to corral their prey, they hunt about 11 hours each night "to get enough energy to do what spinner dolphins need to do", she says.

It is difficult to know whether the decline in whaling has emboldened whales to be more curious about us

During the day, spinner dolphins come into shallow, sandy bays to rest. Peak resting time is 10:00 to 14:00, says Heenahan, making it "peak human time" too.

Resting dolphins do not look like resting humans. They do not lie in bed or shut the bedroom door. During rest, they are still swimming around, making it easy for swimming, snorkelling, and paddle-boarding tourists to mistake dolphin naptime for playtime.

There is also "a large industry dedicated to interacting with and swimming with these dolphins at a critical time", says Heenehan. That, she says, makes it a bit like "a party in their bedroom every night".

For that reason, she is part of a research collaboration studying spinner dolphin activity and acoustic communication patterns, in the hopes of uncovering solutions that work for both dolphins and humans.

There's really no data on whale behaviour before whaling

Whether this daily disturbance is having a long-term impact on this Hawaiian spinner dolphin population remains to be determined. But it is one of the many examples leading wildlife tourism researchers, including Lusseau, to conclude that we need a more precautionary approach to watching marine life like whales and dolphins.

Beyond the unusual friendly encounters at Laguna San Ignacio, it is difficult to know whether the decline in whaling has emboldened whales to be more curious about us.

How whales behaved around humans before we began whaling is a bit of a mystery, explains Christine Gabriele, a humpback whale researcher with Glacier Bay National Park, Alaska. Aside from tales like that of the devilfish, "there's really no data on whale behaviour before whaling".

We just do not know whether they approached vessels or not, she explains. "On an evolutionary time scale, whales had no experience and no opportunity to adapt to something as big and fast as a modern ship."

In many parts of the world, our relationship with cetaceans has changed dramatically since the days when our main goal was to kill them. As our knowledge grows about how prying human eyes impact their lives, we still have much to learn about the art of benign and respectful observation.