To answer the question, I don't think that I'm immature for watching cartoons. I'm 20 years old and I've watched cartoons for ages. I never saw a real reason to stop it since I've enjoyed a lot of them. I've never understood the idea that you can't enjoy a show unless your within the target audience that the general public has with cartoons. I've honestly tried watching the shows that are geared more towards people my own age, but I couldn't really get into them.
As for immaturity, that doesn't come from what a person watches. That has more to do with how a person acts in situations and towards people. I would be seen as a more shy, probably odd, hopefully friendly and quite kind of person than immature. While I usually don't tell people my interest, that doesn't mean that I'm ashamed of it. It's more like a safety net. I've been bullied for what I like, especially Pokemon back in the day, and instead of putting myself in a vulnerable position with letting people know what I like, I keep it to myself. With the exception of my parents of course. It works better for me. Though, the fact that I don't like socializing probably helps, which also goes back to my shy and quiet traits that I mentioned.
So basically, my answer would be no.