I lick my cat
What is your reason for licking your cat in the first place?
Because it gives me pleasure to do so.
I'm worried you may get sick from doing that.  Licking an animal's fur is very unhygienic.  I think you should stop doing that in the future!
It's fine. She's not getting sick.
It just does not seem like a great idea to lick the fur of your cat or animal at all. Depending on what you find gross i guess it may be fine, however you never know what may be on your animals fur. Just does not seem like something that would be smart to do.