My mother once convinced me to accept a Fender T-shirt from her (I'm more of an Ibanez guy, but still better than Gibson), otherwise unless people pay me I won't wear an "advertisement" T-shirt.
I don't mind wearing shirts with brands on em, just not clothing brands. I love wearing tshirts with old company logos or weird stuff like froot loops or a vintage coca cola shirt.
I'll second that, I'm a fan of shirts from local establishments. I have one of a record store I like (actually two, one each from two diff local record stores), a couple local restaurants that are legendary hole in the wall types, local minor league baseball team, etc. I'm not gonna wear like, supreme, but some stuff like that is ok imo.