An August 1973 storyline had Snoopy challenging Hank Aaron for Babe Ruth's career home run record...and getting hate mail telling him "go back where you came from" and "we hate your kind", similar to what Aaron was getting in real life.
Snoopy: I just want to be a credit to my breed!
"NO DOGS ALLOWED!"
Snoopy also has Charlie Brown write a letter to the producers of a TV cartoon complaining that the animal characters were portrayed as "silly and stupid", and also considered boycotting their sponsor.
On the other hand, Snoopy does have an irrational fear of snakes.
There's also his hatred of cats (which could be justified because the cat living next door is genuinely mean and scary, although Snoopy goes out of his way to provoke him). He "celebrates" National Cat Week by loudly booing. And he and Woodstock once made a list of all the things they loved about dogs, using a huge sheet of paper; and then pulled out a tiny scrap of paper for listing all the things they loved about cats. ("We'll probably have lots of room left over.")
Snoopy can also be a Boomerang Bigot, as in an early strip in which he declares he's tired of being a dog, he's tired of associating with dogs, and that if he were human he wouldn't even own a dog.