Your child won't be losing job opportunities because they are non-binary.
Your child might be losing job opportunities because they are presenting it in applications.
Most people don't care (even if they do have contrary opinions on relative current events) about working with someone non-binary.
A large proportion of people can't be arsed dealing with difficult employee's - and if someone is presenting this on their CV and/or at interview, its likely to at least appear, as if they could be difficult in the workplace.
The fact is, no one really cares what others do in their private lives. It's when it can impact work, that they care. Being non-binary tends to become such an intrinsic identity to a lot of non-binary people, that, seeing as it has become their identity, it's impossible for it to not be brought to work. By that I don't mean simple requesting certain pronouns, a fairly easily catered for request (albeit a bit of a pain for those who don't subscribe to these views), most will be quite happy to try.
Then again, my experience working with a non-binary person was very easy in that respect. I did my best, occasionally made a slip up, apologised once, and although it happened afterwards too, never needed to apologise - the person made it clear they appreciated, and could see that I was trying, it can be difficult, and the odd slip is fine. If they had made a huge drama out of it, it'd be another story, and my patience would wear thin extremely quickly - and it's not something I have the time or inclination to deal with. Lucky then that I'm not in charge of hiring.
Sorry OP, I find it all a load of silly nonsense, as do many others - I'm voicing this only because its relevant, and you asked. I wouldn't offer this unsolicited - Whilst those like me still try to be accepting and outwardly respectful whilst holding these quiet opinions, a lot of us just can't be bothered with it. The only one that really cares is the person identifying as non-binary.
I wouldn't not interview or hire someone because of gender identity etc. I would probably not hire them if they appeared very full on about it, and I imagine my team would thank me for it. Same if someone made a big fuss about anything else rather private, actually.
If they're putting stuff about it on their C.V or in interviews other than 'my pronouns are x, y or z', tell them to stop.