The UK should "set an example" by not allowing a planned state visit for Donald Trump to go ahead, a Welsh Labour MP has suggested.
Paul Flynn opened an MPs' debate on the visit on Monday after two petitions received more than 100,000 signatures.
But Conservative MP Glyn Davies said it was perfectly reasonable for the prime minister to invite Mr Trump.
Hundreds of people attended anti-Trump protests across Wales, including Cardiff and Swansea, on Monday evening.
The debate in Westminster Hall took place after two petitions - named Prevent Donald Trump From Making a State Visit to the United Kingdom and Donald Trump Should Make a State Visit to the United Kingdom - crossed the 100,000 signature threshold to be considered in Parliament for discussion.
One received 1.85m names, while the other had 311,000.
Mr Flynn, MP for Newport West and a petitions committee member, told the debate there was "no question" of disrespect for the US but there was "a great feeling of concern that welled up" in the petitions.
He said protests were "an expression of fear and anxiety that we had someone in the White House wielding this enormous power".
"We've had people here who are very unsavoury characters... certainly we can't try to imitate the errors of the past, we should set an example by making sure we don't make those mistakes again," he added.
Cardiff South and Penarth Labour MP Stephen Doughty told the debate: "We have a special responsibility when it comes to the special relationship.
"We cannot accept the denigration of a free press, the denigration of a judiciary, the denigration of women, the denigration of religious minorities, the banning of refugees, the advocation of torture as the new normal."
But in response, Swansea-born Nigel Evans, a Conservative MP for Ribble Valley, said MPs at the debate "cannot understand why it is that the people voted for Donald Trump, why people voted for Brexit".
"Until people in this room understand that, then I'm afraid there's going to be more of the same," he said.
"The people who feel left behind have spoken and they voted for Donald John Trump."
Earlier, Montgomeryshire MP Mr Davies told BBC Radio Wales it was "perfectly reasonable" for Mrs May to invite Mr Trump for a state visit.
"I'm no fan of Donald Trump, his style of presentation and speaking, there are a number of things he's said that are offensive," he said.
"But he is the president of the United States, the people of America have elected him as their president.
"The relationship between Britain and the US means that he is going to be a very important ally and a very important partner from a security point of view and probably an economic point of view over the next four years."
The UK government has said it recognised the "strong views" expressed by the US president but looked forward to welcoming him once details have been arranged.