There's a type of man that has plenty of time to watch children's movies: a father. (Or you could just watch them because you enjoy them and not worry about what people think).
it's not about what others think of me. It is about what I think of myself.
Watching this kind of stuff sends the wrong signal to one's subconscious ... that one is still a "child"... and this will show up in one way or the other in one's interaction with other people.
it's already not so attractive to watch TV and even less attractive to watch anime or other children stuff on it.
This might hurt to hear, but you're a coward if you let gender roles stop you from enjoying something.
I sincerely recommend reading some theory on gender. Gender Trouble by Judith Butler is a surprisingly approachable introduction to the subject, despite not being written as such.
You could police your identity to make yourself attractive to someone that you need to hide yourself from for the rest of your life, but it's a tremendous waste of energy. Find yourself an anime girlfriend.