The Beasties actually did dress up in Classic Trek uniforms for one of their videos, for the song "ch-check it out" I think. They ran around a modern street like they went back in time, chased around a bit, then ended up killing each other with phasers. Kooky stuff.
They are big Trek fans, and often reference the show in their lyrics.
Like a pinch on the neck from Mis-ter Spock.