I think the problem is that (rather ironically) it's not the binary issue that so many people portray.
On one side you have some folk claiming that it's never appropriate and it's always just silly, and on the other you have people claiming that it's perfectly natural and doesn't ever cause any issues at all.
I think for native English speakers the truth is somewhere in the middle.
They/them can be used effectively and naturally in many conversations. However, at times, the use of they/them can sound awkward and slightly odd, and it can make it difficult to follow a conversation, especially when there are multiple people being discussed.
Eg/ "Joanna is having trouble at school as they haven't been given a timetable yet. The teachers don't have it either. They don't know when they will receive it."
Joanna uses they/them pronouns. In this example, who does the last "they" refer to? The teachers? Joanna? Could be either and it's very unclear. This is an actual real life example. They would normally be plural and therefore would more accurately be used to described her group of teachers. However, because Joanna also prefers they/them, the plural-sounding pronoun in this example could also be referring to her. However, the "they" in the first sentence is fine as we all understand it clearly refers to Joanna.
I am aware this is a shit example but a) this actually happened a couple of weeks ago and b) I'm not awake enough to think of something else 😂