Well, might as well.
In my opinion, I think they wouldn't if they're just playing publisher and the game was from a 3rd party dev. Bayonetta 2 and Devil's Third was released under with Nintendo's marketing, funding, and support, and those games have a lot of adult content. I'd question more why they're publishing that game in the first place, considering the overall themes and history of the series.
In the case of Fire Emblem, it's a game made by a Nintendo 2nd Party that is basically deeply rooted in the company. Fire Emblem is a valuable Nintendo IP that is directly connected to them as their product, so any negative attention reflects back on them, not Intelligent Systems. Said negative attention can lead to loss of sales and hurt their branding.
I fully accept video games as art, but publishers are a business first. They want money, and they see pandering, marketing, and localizing to the region's culture, language, laws, political climate, and history to make sure they have the best chance of profiting. Is that censorship? No, for many reasons. The original still exists, and you can get it the way it was released in Japan. The American version is a different version, its contents are altered justifies it as its own thing. That's known as Derivative Work, a thing that exists in the Art World and something I fully partake in. There's no removal of something if that something still exists elsewhere. Censorship is the complete ban of the content, you can still import games and consoles from Japan if I recall. No one will stop you from learning Japanese, and buying the game and 3DS on PlayAsia, not Nintendo or the United States government.
What you want is the original completely translated into English, what Nintendo wants is to release a game that makes them the most profit in the region. Just say the truth, it's not censorship, it's Nintendo not pandering to your and other gaming enthusiasts' tastes, but rather the entire region as a whole. This leads me to my next point.
Let's be real, the loss of sales they'd get for removing this garbage subplot is not as bad as the potential outcry from the LGBT community and a lot of other groups. Nintendo already has a bit of an iffy reputation with them and this subplot seem like conversion therapy to some, which is a very big issue that a lot of LGBT youths go through here in the United States. Combine that together and there's a good chance it will hurt their brand far more than a handful of people screaming "won't buy cause censored".