Sure, it would never make sense from any viewpoint for Star Wars and Star Trek to meet. Star Wars was all about rollicking adventure, dashing heroes, and simple good vs. evil battles across space and land. Star Trek was all about philosophical quandries, the issues of a utopian society, and lots of talking about big ideas.
...until JJ Abrams basically turned Star Trek - which once had a movie all about the crew of the Enterprise trying to save some whales - into his audition for Star Wars. So yeah, the rebooted Star Trek totally fits with Star Wars.
(*to be read in Benedict Cumberbatch's menacing "John Harrison" voice*) Shall we begin?