I'm right handed and left eye dominant. I shoot both handgun and long gun right handed. It's never been an issue.
First of all, it depends how bad your vision is in your weak eye versus your strong eye. Not everyone is the same and no one solution will work for all. To say just deal with it is not the correct answer. I have trained enough people while in the Army to know that it does make a difference.
Is it an issue for surgeons or dentists? For machinists or auto mechanics? Nope. So why fret over it here? It's only an issue for trainers who have little experience of the world. About 1/4 to 1/3 of the world's population is cross eye dominant. Most don't know it because it's never an issue even when doing delicate work. It's a bigger issue if you're left handed.
It's not always the same and is comparing apples to oranges here. I am a retired machinist/tool and die maker.
With hand gun I focus through the dominant eye. My stance and and a slight tilt of the head do the rest.
Most of us that are cross eye dominant do the same thing. Use strong hand and strong eye for handguns.
With long gun I close the left eye while looking through a scope or over peep sights. If shooting at a range for a couple of hours I may use a blinder over the left eye to avoid fatigue in that eye.
You can have a dominant eye even when vision is the same in each eye. In that case, you can train your non dominant eye to focus on the target. Now if you are bench shooting, then cover the one eye. Use what method works the best for you.
It's never been an issue and normally isn't until a person makes it one. Usually the person who makes it an issue is the person who first trains you. They learn you are cross eye dominant and they say, "Well that's an issue but I have a solution to that problem." But they don't cause they don't know what they are talking about.
It is proven that if one eye is a lot stronger than the other to shoot using your dominant eye even if it is on your weak side.
"But you have to keep both eyes open". What, all the time? No you don't. That useless "tactical" idea is fairly recent.
This is incorrect. I have read enough Army training manuals along with training troops to know that this has been standard procedure for a long time, at least since late Vietnam.
No one has to learn to shoot with the weak hand because they are cross eye dominant. Unless they only have one eye, or one good eye but that's a whole 'nother issue.