My Dad is right handed and his dominant eye is his left. He's done ok as a competitive shooter over the decades, and a few years back got bronze and silver successive years shooting pistol in the Senior Olympics.
I'm lefthanded, and all my modern rifles are right handed. I also have several right handed black powder rifles. Even though the black powder rifles I grew up shooting were right handed flint and percussion rifles, I do enjoy the lefthanded flint rifles I have now.
I do many things righthanded already, and my better eye is the right one, so I forsee the possibility of either shooting righthanded, or lefthanded with right eye. I've tried both and either way is doable should the need arise.