Germany's players covered their mouths during a team photo ahead of their 2-1 defeat against Japan to show "Fifa is silencing us" by shutting down attempts to wear rainbow-coloured armbands.
Seven European nations, including England and Wales, abandoned plans to wear the anti-discrimination symbol after Fifa threatened sporting sanctions.
The Football Association declined to comment on whether England would copy the German gesture, which could result in disciplinary action, ahead of their match against the United States on Friday.
Fans in Doha were also split over whether the home nations should follow Germany's lead.
England fan James Fogarty, 39, who lives in Connecticut in the US but originally from Tunbridge Wells, Kent, told the PA news agency: "We knew what we were getting, right - the World Cup shouldn't have been here but now it's here, it what it is."
Asked about the armband row, he said: "One of the things that's slightly irritating is you go into the fan shop, you go into the stadiums and you can only pay by Visa, you can only drink Budweiser, you can only buy Adidas shirts and Fifa has sold out, right, and Fifa have sold out to the Qatari royalty too.
"They're clearly not running the show, the Qataris are running the show and that's unfortunate."
On whether England should follow Germany's protest, Mr Fogarty said: "Like my son said, the Germans have got a bit of history themselves and no country is perfect.
"I don't like it when pop stars preach to me about politics, I don't necessarily want football players preaching to me about politics.
"We know we shouldn't be here, I wish they'd just play football."
Ryan Tobin, 29, from Bridgend, South Wales, expressed concerns about rainbow bucket hats being confiscated from fellow Wales fans.
Mr Tobin and his friend Dylan Thomas, 28, from Maesteg, South Wales, said Wales captain Gareth Bale probably should have worn the One Love armband to send a signal even if he risked being booked.
Asked if Wales should follow Germany's lead, Mr Tobin said: "Yeah, why not? It makes a statement, doesn't it?"
Mr Thomas added: "It's important to show you're together."
Joe Lyddon, 31, from Wrexham, said: "I thought they should have all just worn the armbands to be honest and just taken the yellow card.
"If they're that serious about it, I think Bale got booked and would have got sent off but that's the risk you've got to take."
Fans have reported having rainbow items, including T-shirts and Wales bucket hats, confiscated by officials in Qatar during the tournament.
Rainbow-coloured corner flags emblazoned with the Welsh dragon appeared on the team's training pitch in Al-Sadd, Doha, on Wednesday.
Foreign Secretary James Cleverly said gay rights is an issue he has "brought up over a number of years" with Qatar.
He told the BBC: "I've made it clear that we feel very strongly about this issue and, actually, one of the advantages about having a strong relationship with other countries is you can have these difficult conversations.
"The Qataris know how seriously we take this issue and they have taken real steps to ensure that gay football fans are safe and do feel secure and can enjoy the football."
But several LGBT+ supporters have opted not to travel to the tournament in a country where homosexuality is still illegal.
Downing Street said it is closely monitoring the treatment of UK fans at the World Cup.
Conservative MP Alicia Kearns, who chairs the Commons Foreign Affairs Committee, said hosting the World Cup will not deliver meaningful change in Qatar.
She told MPs: "Qatar has shown since it received the nomination to hold (the World Cup) that nothing about their behaviour has changed domestically or even regards to workers.
"So I really don't think, unfortunately - and I wish this was not the case - that we can have any hope that things will meaningfully change."
England goalkeeper Jordan Pickford, when asked about the armbands controversy on Wednesday, said: "As a squad we all had conversations and we all stand for it. We all wanted Harry to wear it, but I think the decision got taken out of our hands as a squad and as players. It went higher up than that really."