It depends, I think japanese developers and japanese fanbases tend to ignore them most of the time since they're are seem mostly as a bunch of hysterical harpies who derail every kind of legitimate conversation about the series they're fans of. Unless, of course, the series in particular is geared towards them, which in case there's no helping.
Western fanbases tend to be more forgiving and since most of them are girls there's some people who use the sexist card to defend their actions, all in all i think the main difference of the western fujo is that she knows how to use idpol to her advantage better since none of the "male" fans would want to look "homophobic"
In any case, they're extremely annoying should be shooed away whenever possible.
It's kind of hard to say, gay characters in FE are nothing new, some old games (like SNES-era old) had characters that are gay but they're never the annoyingly flamboyant, in-your-face kind of gay.
The problem is the fanbase itself, since the game allows you to play "matchmaker" with characters other than the MC it becomes a nesting ground for the worst kind of internet dwellers, like fujos, furries, tumblrites and other kinds of bottom-feeders, who fight over whose "ship" is the best and which character is a "gay icon" or any other crap.
If I had to recommend a "safe" FE I think Sacred Stones for the GBA would be a good start, it's neither too old nor too new but enough fo you to feel the hang of it, and of course, no "surprise" characters.
Awakening, ironically, is also technically "safe", the only character who raises an eyebrow is the goth mage girl who simps for your character regardless of gender, but she can onle be romanced by the male MC anyway so there's that.
I've never played the GC ones but I would stay away from it, the discourse of these games is tainted by fujos who are convinced that the MC is gay just because he never hooks up with anyone.
There's also the older ones, these tend to be a little bit harder but you can try them if you want.
I would buy Intelligent Systems and force them to make a new Fire Emblem game, however this time there would be no homo romance between any of the playable characters, not even in subtext; Then, I would specifically order them to make one of the villains an extreme caricature of a gay man, think of the most extremely unflattering stereotype, just so he can die a very painful death in the end.
The reason? Simply so I could get rid of all the faggots, trannies and fujos that have infested the community ever since Awakening. It would be a huge shitshow, they would be so outraged that they would probably ditch the series completely.
After all that IS would release another FE game, but this time it would be an actual tactic RPG instead of a glorified dating sim.
One of the worst things that humankind did (or rather, failed to do) was failing to punish female homosexualism with the same ruthlessness and scorn that male homosexuals got. Most gays that I met were normally pretty chill to be around and normally would behave, probably because they know that if they messed with the wrong guy they would, at best, get their asses kicked and, at worst, killed. But lesbians? Holy fuck, you won't be able to find the most unpleasant, crass, disgusting and obnoxious people even if you tried. Imagine a woman, with all of her worst aspects, then add the worst aspects of a man, then add a pathetic feeling of superiority just because she's not fighting other women for dick, there, now you have the 'modern' dyke, and the worst part? They know that the institutions protect them, they know that you can't do jackshit to them, they know that they can act like histrionic bitches and do the most degenerate crap without fear of reproach because if anyone dares to critisize them, they can just call him homophobic, racist, misogynist or whatever buzzword they come up with, make him lose his job, get arrested or even worse.