Nice topic. I am one of those people who distanced myself from animated films as a teenager, growing up during the 90's.
I guess you could say they were "uncool" in the sense that my friends would probably have made fun of me for watching them... but truthfully they just weren't really on my radar. I think people at that age tend get focused on grown up things, as you said. My friends at the time were all into live action/shoot-em-up/comedy films, so that's basically what we watched. Animated films were never discussed.
I remember in 2001 when Shrek was released, suddenly animated films were hip with teenagers again. I thought it was just an OK film. Later, I saw and Monsters Inc., then Ice Age in theaters.... but I'd say Lilo & Stitch is the film that really got me hooked on animation again. Ebert gave Lilo & Stitch such a glowing review that I actually went to see it alone.