YABU, use the pronouns they chose for themselves or stop using pronouns altogether when referring said friend, especially in her face. I promise you, it isn't that hard.
Example if you can't use ''they'' to refer to Sarah, next time you want to refer to Sarah in front of Sarah or introduce her say '' Hey Nathalie, long-time no see, let me introduce you to my friend Sarah, we have been friends since high school, Sarah this is Nathalie, a colleague'' (absolutely no need for pronouns anyway!)
''Yes mum, I am with Sarah right now." (Again no need for pronouns).
Talking about people in front of people shouldn't happen often anyway, so you might want to revisit that.
People who are autistic get a pass I say for obvious reasons but if you are not autistic or suffering from any other diagnosis that might impair your ability to do this, you are being very unreasonable and quite a bad friend.
Not sure why someone wanting to be referred to as something else than their original name/pronouns is making you ''very uncomfortable'', most people have nicknames or names that have nothing to do with their birth name due to not liking their actual name and I don't know anyone who feels uncomfortable by it. Wouldn't you feel very ''uncomfortable'' and upset if someone was continuously misusing your name or referring to you as ''they'' when you have repeatedly told them you do not want to be referred as such? If that would upset you why not feel understanding towards your friend as to why they feel upset you continuously mis-refer to them?
I suggest you watch this whole webseries (found it very informative as someone who is a she and initially had trouble with using they) but if you can't/don't want to watch the whole thing, definitely watch this episode, I think they do a brilliant job when it comes to explaining how it works and how not hard it is, though it might come across as impossible at first. (Obviously it's a comedy and for comic-relief purposes so not meant to be 100% serious nor realistic but the messages, issues and explanations this webseries bring to the forefront is definitely valuable, regardless of one own personal beliefs (or disbelief) and opinions of non-binary individuals).