It's not that Star Trek fans or even Star Wars fans are anti-intellectual. It's that they come to these kinds of sites to discuss one of their favorite genres. There are still intellectual discussions here, but they don't always use an element of Star Trek as their subjects. On this site alone, you find insightful dialogues on crime, human rights, contraception, physics, philosophy, and whether Spock's left ear is a millimeter taller than the right.
Not by definition, of course not but all people, ST fans, SW fans, ST & SW fans and fans of neither can be at times anti-intellectual. Human nature. Emotionalism wins over thought more often than not. It does seem that comment boards on the internet, whether here or Facebook or CNN or anywhere else, where comments and/or discussion is allowed, inevitably attract and succumb to a level of anti-intellectualism simply because people get extremely passionate about their opinions.