We have done some custom shirts with characters (like the still from "Lilo and Stitch" where they are on a cruise ship) and have never had any problems. I think they only get upset if you do it for profit rather than personal use. Also, the store where we have them made is a little cautious about copyrights. They will only do a certain amount to ensure you are just having them made for yourself and maybe your family.
Barb