One thing about Traditional Archery— there is no shortage of experiences and beliefs!
I, for one, agree with Jay Kidwell and his view in his book, “Instinctive Archery” where if you shoot “instinctive” dominance doesn’t matter.
If you use any sort of aiming involving the arrow (gap or gun barrel or whatever else it’s called) that is a whole different story.
I’m like you, Right handed and left eye dominant. As long as I stare at what I want to hit, when I come to anchor, as in Jay’s book, my shaft is rather between my eyes and as a binocular, front eyed predator, dominance has not affected me.
Shooting sights, I don’t use them or shoot guns or bows w/ peeps so whenever I pick one up, I have to close my left eye to make my right eye look at the sights.
Shooting trad, instinctively, not an issue. YMMV