Can I tell you my secret?
You can tell me your secret, I won't leak it. I promise!
I secretly like anime
You can keep that secret from others. It's not bad having something you like be kept a secret.
How would you feel if I tell this secret to everyone in the class and the school?
You could tell anyone you want, but if you want to keep it a secret then that is fine too. You're always allowed to keep innocent things like enjoying anime a secret, and no one should care either way.