The answer to that is probably 'we don't know' - there's nothing inherently wrong with using 'they' and 'them' as your pronouns, but we don't know the effect having this sort of very binary 'right' and 'wrong' has on teenagers. The rigidity of thought Derek has commented on has been my experience when discussing the issues with anyone under the age of about 25. There is no room for discussion, there is no room for nuance...

I don't think it's helpful to bring anyone up under a fundamentalist and absolute system. Liberalism is fast becoming an absolutist system akin to a religion, it has followers and converts rather than rational pioneers prepared to discuss. It's a worrying direction for teenagers to go in. Using 'they/them' isn't itself a problem, but I'd suggest it shows a worrying direction of travel for young people divorcing themselves from the capacity for rational discussion and enforcing an exclusionary mode of being on the adults around them.

I'm worried, but I can't put my flipper on exactly what I'm worried about yet. :o)