I’m going to say it depends… on shotgun, I generally teach students to shoulder on the dominant eye side. For some folks, rifle works better that way too.
Some folks will be able to retrain the non-dominant eye to be in charge using the tape-on-the-glasses things, but there are some for whom it doesn’t work, or who can’t do it for other reasons.
My hubby is strong right eye, and a retired serious competitor with millions of rounds down range (not exaggerating). He lost most of the sight in his right eye to a detached retina but his motor skills are all right-hand right-shoulder. He has his rifle scope mounted on the left of the rifle at a 45 degree left cant from the normal position… that works for him, but it does cause some issues with adjusting distances. (that’s partly scope mechanics and partly his loss of binocular vision which affects distance perception.) His accuracy is amazingly good, but his acquisition is a lot slower than it used to be, so while it works, it’s not a solution that would work for everyone.
For pistol, turning the head to align the dominant eye over the barrel can work well for some folks (that’s what my hubby does) if they can’t get the eye to switch.
There are some folks who cannot seem to manage either the head turn, or getting the other eye to take over and for them, I have them change to their non-dominant hand. That actually seems to be a very short learning curve, and more reliable than getting the other eye to take over for some people.