As someone who has been to a few pride events (not like the big big festivals, but smaller local parades and small rental place event), I never really thought about wearing any of my furry themed stuff to said events. I think my reason being that I find these two elements of my life to be unrelated and not necessary to be mixed together. It's kind of like my job and my gaming characters, I wouldn't make my job title a character in a RPG or MMO because I feel these elements of my life are unrelated, you know what I mean?
P.S. I have no problem with anyone who chooses to or anyone who chooses not to. I feel like this is merely a personal preference and there is no right or wrong way to go about this.