Catalans Dragons say one fan was asked to move a rainbow flag during their match against Castleford Tigers because it covered an advertising hoarding.
But two women said they were told to remove similar flags - a symbol of LGBT pride - "on health and safety grounds".
The incident came as Israel Folau made his debut for Catalans on Saturday.
"Stadium security staff are briefed to ensure that advertising boards are kept clear throughout the game," the French club said in a statement.
Super League, who said on Saturday that "everybody should have the right to respectfully express their views", stated that Catalans had assured them a thorough investigation had been carried out by the club.
However, the Rugby Football League will undertake its own independent investigation into the matter.
"We thank Catalans Dragons for their instigating their own investigation, but we will need time to consider all the available evidence before reaching any conclusions," an RFL statement said.
Catalans 'welcome flags in all stands'
Catalans controversially signed Folau last month after the 30-year-old utility back had been sacked by Rugby Australia in May 2019 for posting homophobic comments on social media.
The dual-code international scored a try on his first rugby league appearance since 2010, helping Catalans to a 36-18 win.
Castleford fan Alison Grey posted a photo on Twitter of her holding a rainbow flag at the Stade Gilbert Brutus, saying: "Just been told I am not allowed this flag because the club does not allow it. How disgusting #loveislove #castleford #pride."
Catalans said supporters' flags "are welcome in all stands" at their Perpignan home.
"Having reviewed the CCTV footage and numerous photos in the media, we can confirm that supporters were able to display their flags and colours throughout," the club added.
"However, it is important flags and banners do not cover advertising boards.
"The investigation found that one person was asked to remove a flag because it was covering an advertising board.
"The only banners and flags forbidden in our stadium and other sports stadia would be those which are insulting or inciting violence."