Why not ? I like both of them just fine ! I've watched all the Star Wars movies and watched all the Star Trek series and movies. I can't see anything wrong with that.
Can a person like both Star Wars and Star Trek?
How about someone that neither Star Wars and Star Trek interest them ?
I like both of them, although Star Wars is admittedly better :-)
Yes, I like them both but have to admit that I'm a bigger Star Trek fan.
Yes
If they want to.... They can. That's one of the freedoms we still have.
Sure and Battlestar Galatica as well. Matter of taste is an individual thing.