No stigma to being cross dominate . I've shot that way my whole life. Rifle,shotgun lefthanded pistols righthanded but sighted to the left eye . The Weaver stance fixes the goofy across the chest thing. I took up the bow which I shoot righthanded after I suffered blood pressure issue related vision detieration in my left eye . I shoot mostly both eyes open as I never have been able to wink the left 1.

My youngest boy drove the sargents nuts he's a lefty but right eyed shoots both ways.