Yes, any tattoos will significantly hinder your aspirations as a media composer. Especially ones that can be covered up. We spend A LOT of time with other people while we write; that little tattoo underneath your shirt will certainly offend someone eventually. People in this industry are very conservative and have little creative tendencies so any sort of expression is risky. In fact, your outward appearance is much more important than your music so you should spend the majority of your day worrying about how you look.