I don't think I've ever felt embarrassed by my fiction preferences, and I've never felt particularly ashamed of Star Trek. From personal observation, Star Trek used to be 'cool', lost its popularity after the '90s (a trend started by the later films), and now is picking up steam again with the trendy new film (aka Star Trek XI).
I remember attending Halloween parties in the late '80s and early '90s dressed as Data or Geordi (complete with a home-made VISOR), and no one particularly made fun because, well, Star Trek was trendy at the time. Geordi was especially a well-liked character because of LeVar Burton's work with Reading Rainbow, let alone his general social rights work, for which Star Trek had always been a vessel.
That said, I never did wear a Star Trek costume -- or any other costume -- outside of a costume party, simply because, well, I believe in decorum. But I have worn Star Trek T-shirts in public, especially my signed (in print) 25th Anniversary T-shirt. It's nice getting a knowing smile from fellow fans.
For too long people have been caught up on status, style, looks, and lifestyle. I hope one day we can judge people on their actions more than the way they look or what they enjoy. I am a fan of star trek, and a nerd, and I could care less if people think less of me for it. They reveal their own iniquity by doing so.