Ahem, continuing to steer the bus back onto the road, there are so many flavors of Trek that there can be many different public perceptions, but they're general and some are stereotypical. Within fandom, the perceptions are more nuanced and people are more protective of "their Trek" and will often defend it as the "one true Trek" (the only one to believe in if you want to go to heaven).
Dennis had it right way back on page one, "Star Trek" is seen as a niche product by the general public. The fact that you can walk into a toy store or shirt shop and see DC heroes stuff, Marvel heroes stuff, God knows "Star Wars" stuff, "Sherlock" stuff, and such, but seldom, if ever any "Star Trek" stuff speaks for itself.
It's baggage and the belief that that it actually may be a denser, more unapproachable product than it is (because of its incarnations and the canon created by fans) makes it less generally attractive, too.
That's why I believe the Abrams reboot was a stroke of genius. Everyone gets back in on the ground floor. The fun starts here. I literally dragged my oldest daughter (now 16) to ST09 and STID, and while ST09 was, "Surprisingly OK," she became a fan after seeing STID and has actually seen it more times than I have. When I showed her the teaser for STB, she thought it was great. There's the future of Trek, right there. Her generation's perception of it and the enjoyment they get from it are far more important than those of their fathers and mothers (though luckily, I'm at least as enthralled with it as she is). Thinking she can't be a fan because she has never seen TOS or TNG (let alone DS9, VOY or ENT) doesn't mean she's not a fan. She's a fan of HER "Star Trek". Because she found TWOK "a bit slow and talky" doesn't mean I should misperceive her. That movie predates her by 16 years. How many 16 year olds like 30+ year-old movies, let alone a 50 year-old TV show? If those aren't to her taste, I can see why. Her perception of "Star Trek", and the perception of enough movie-goers to make ST09 and STID successful and merit STB, are the future. We, the old farts, have to let go sometime.