I already disliked all the references to US history in Fallout 4. To me, cowboys feel misplaced in a science fiction universe. It’s just personal preference though. But the question stands: are large parts of the main story related to the cowboy characters, or does it work mostly without?
Starfield, like a lot of sci-fi, compares the early days of space travel to the old west. With that said, at close to 30 hours in my first character, there hasn’t been a single time I’ve engaged with the cowboy stuff. It’s largely attached to one of the two biggest factions, which is a group I haven’t engaged with at any point so far, with one exception being an encounter with one member of that faction as part of a brief, radiant quest.
So yeah, you can completely avoid it! Happy gaming!