Yes - no matter who you side with, you can still talk to them afterwards and access their shop. It would just take you a little longer to open up the full catalogue of items that are sellable by those faction vendors - since some of them are tied to what your reputation is with that faction.
I suggest you side with the faction that sells you the items that you really want so you can unlock them faster. I.e. if you want the gauss minigun, side with the Raiders. If you want the gauss shotgun, side with the Settlers. And so on :)