We expect people to say things that make them uncomfortable all the time. I don't feel comfortable telling my boss that I'm the one who wrote the buggy code that caused the incident, but I have a responsibility to do it regardless. I might be expected to thank everyone involved in a project, even if I don't feel personally grateful to them. And so on.

Obviously there's no easy way to reason these cases from first principles. As it is, I'm aware that being affirmed in their gender identity is recognized as therapeutically important for trans people. On the flip side, I'm not aware of any condition that causes people to suffer significant distress due to using a particular pronoun. So in this case, I feel like it's a pretty easy decision.

EDIT: The "neopronoun" question was added after I replied, or I missed it. I have never met a person who expected me to use them, nor have I ever encountered a workplace environment where policies required their use, so I haven't formed an opinion.