I haven't read all the responses since my last post, but to pick up on this...
I may be wrong as to what a court would find reasonable. Until there are some actual court decisions, the best any lawyer can offer is an informed guess. However, below is what I think a reasonable policy would look like. I'm going to use a word I detest - misgender. Apologies to anyone who is offended by this word. The only reason I'm using it is because it has a clear dictionary meaning (even if we disagree with it) and makes it easier to express what I think a reasonable policy would be.
I think a reasonable policy would be to say that you must not be offensive to a trans individual by deliberately misgendering them to their face or in their presence. Therre would need to be reasonable exceptions to that, so this is far too simple, but it makes the point I'm trying to get at.
What would that mean in practice?
When talking to someone, we don't use their pronouns at all. It would be very odd to refer to someone you are talking to as "he" or "him". All the policy is doing, therefore, is stopping you gratuitously working pronouns into a conversation.
When in someone's presence, we sometimes use pronouns, particularly when we are talking about them to someone else in their presence, but most of the time we don't. Importantly, this policy is not forcing you to use their preferred pronouns. So, if I am in a group of people including Upton and we are talking, I could call him "Upton", "Dr Upton" or "Beth". I don't have to call him "her" or "she". My view, which I think the courts would share, is that this is not forced speech because you aren't being forced to use his preferred pronouns (and you shouldn't face disciplinary action if you use the wrong pronouns accidentally). You may not like calling him Beth, but there are a small number of non-trans men with that name, and we are all allowed to use whatever name we want.
For most employers, I think the courts would probably accept that as a reasonable policy. I may be wrong, but I doubt they would accept as reasonable a policy that attempted to force you to always use the individual's preferred pronouns.
In this case, SP referred to Upton using his preferred pronouns and preferred name except when trying to explain to him why she wanted him to leave the changing room while she got changed when she was experiencing menstrual flooding, and possibly when talking to HR. I think the courts would find that a policy that did not allow her to behave as she did was unreasonable.