YTA. Not because you're peiotizing your FMIL but because of how you handled the situation. Asking your friend to just come without her *SERVICE animal is literally asking her to put her life at risk for you. It's okay to say that your FMIL is a priority so she shouldn't attend the wedding, but asking your friend to potentially die is unacceptable. She's not overreacting to the request and I'd be surprised if you still have a friend after this.

I also have to wonder if you're prioritizing FMIL just because it's the wedding or if this is going to be an all the time thing, which your friend is probably also wondering. How many things will you exclude your disabled friend from? All celebrations? Holiday parties? Your own birthday? Anywhere MIL might be? What does your FMIL do if she goes out to a restaurant or something and a stranger with a service animal shows up? At some point she needs to accept that she needs therapy for this phobia. But will you just exclude your "close friend" from your entire life after marriage simply because she doesn't want to choose between life and death to be around you? Where does it end?