I'd be interested on your take on the large number of students (mostly biologically female) who insist (i.e would report me) if I don't refer to them as they and identify as non-binary. That's the biggest driver here for people using pronouns. A student led push to add pronouns changes in the internal version of zoom for the university used the link to explain to oldies like me https://lgbtlifecenter.org/pronouns/#columns-11*
In my inarticulate way this what led me and other male colleagues to add (he/him) something I've now already removed from email and will take from my zoom, especially as we go face to face for most classes nowadays.
Is the case, ONLY LGBT non-binary should update pronouns to remind the hetro majority they are uncomfortable with he/she??
I ask with all genuineness and not trying to score points or anything, I genuinely need to think about this a lot more than I have in the past.
My advice on this based on where it seems the law currently is would be to respect their pronouns and make an effort to get it right.
Obviously, you'll slip up from time to time and I know from personal experience that it can be a real struggle dealing with groups of people with lots of different pronoun iterations, especially when people change them from the ones you've just got to grips with and when odd combinations come up like "they/hem", etc, where it's hard to tell if it's a zoom typo or a conscious choice, and so on.
I would take it as a request students are making, akin to stating a preferred version of their name, etc, so while it's massively challenging, if you're seen to be making an effort, then it protects you somewhat if anyone reports you for messing up, as it's clearly not malicious.
Respecting other people's pronouns is a distinct issue from stating one's own, and you are perfectly within your rights to refuse if your boss insists (with no explanation needed).
When considering what's most sensible legally, I think it helps to move away from thinking about classes and groups and who's inside and outside of them, and view it more in terms of mutual respect - as in I will respect others' choices and make an effort to use their preferred pronouns, and in return I expect them to respect my refusal to state my pronouns and to respect my right to a privacy and freedom of thought, etc.
I think it's not so much that only trans/non-binary people should add their pronouns but more that (1) it is a deeply personal decision to do so and should never be mandated by an employer, colleagues or students and (2) non-trans men also need to give careful consideration the impact on women (who are protected from sex discrimination and harassment under the Equality Act) of stating their male pronouns. Men have more of a responsibility than women to carefully consider this issue wrt stating their own pronouns because of the inherent power imbalance between the sexes.
I definitely think as a man, you've made the right decision in removing your pronouns as it can be really upsetting for women (and non-binary female people who don't identify as women) to see that. Some students will want you to add your pronouns, but for every person who does, you will potentially be offending hundreds more. Plus, in your field, it absolutely makes sense to think this through carefully (as you're obviously doing) as others will be looking to you as an expert in this stuff.