I'm in the camp of thinking that anyone in the Star Wars universe can have power in the Force, but there are different way in which it can be gained. The Jedi can gain power in the force through their Yogic practices and the Sith can gain it quickly through these same practices plus an aggressive mindset. In my personal view, nobody is born with ability in the Force. Aside from being a pretty good pilot, Luke had no special Force abilities until Ben began training him, and Leia didn't have them until Luke suggested the possibility. Genetics may predispose someone to being more suggestive to the Jedi's training regimen, but that is about where genetics ends for me in being the basis for Force sensitivity.

I believe that some people in the Star Wars universe (Rebels) see the Force as a sort of sentience, a Godlike power if you will, that people can gain by fighting for a just cause, which is why the rebel commanders will say 'may the Force be with you'. Whether or not that aspect of the Force actually exists in this universe is up for interpretation.