Do you want to know:
If one shoulders a long gun sighted in with the dominate eye on their strong side, then switches to the opposite shoulder and eye, does it affect the POI? No, not that I have found in training and competition .
I saw a beautiful woman get her face beat up because of cross eye dominance firing a 12 ga. shotgun while shooting slugs. Right handed, left eye dominant made het lean her head over the comb of the stock in an attempt to aim. 10 rounds later swollen bloody nose and right eye swollen shut, black eye! Now that really did change the POI due to a$$ whoopin' she was receiving! She got cleaned up, tape over the left eye piece on her shooting glasses, re shot that course of fire and qualified.
No difference with handguns, however I keep 99% of my shooting under 50 meters.