Although if i did use "You're a nazi" like the way you suggested it would also work, but "your" would be much shorter, and I'm also more used to using "Your" in my everyday life.
For example, if I was to say "Your drawing is nice", "Your" would be a better word to use than "You're" because saying "You are drawing is nice" would not be accurate grammer.
"Your" and "You're" are actually both English words, one of them is just a term for possession while the other is a shortened version of "You are" though both STILL works in this context.
