No it wouldn't. They/them is already a singular genderless pronoun. It's used as such all the time.
"If you encounter a person and see they're in need, you should help them."
Absolutely nothing new or unusual about it. The pushback is entirely from discomfort with non-binary people.
To preface, since there are so many trolls who talk about this subject, I always have and always will call people by whatever pronoun they want to use. It's just the right thing to do, and that's all that needs to be said about what people want to be called on an individual level.
That being said, the language would benefit from having a
dedicated genderless singular. Even outside the realm of non-binary people there are a variety of situations that I've seen crop up in my life where people genuinely thought there was a group of people being referred to, when the conversation was only refering to a single person, because they is more commonly used to refer to groups of people. This isn't an argument that it's grammatically incorrect
or that we shouldn't refer to people who want to be called they/them as they/them. I'm just arguing that a dedicated genderless singular would make the language more accurate. But it's probably too late on the one hand (so much of the language is set in stone) and too early on the other hand (too many assholes in society to make it possible to introduce new options for pronouns).
Still, at this point the best thing to do is just to say they/them, because that's probably the most likely to be accepted, and a lot of non-binary people want to be referred to by those pronouns. I'm just saying that wanting a dedicated singular doesn't have to be an argument about historical use, grammar, or necessarily even someone being an asshole.