Cross eye/hand dominance is not as uncommon as you'd think.
If on the range,, you can put a piece of Scotch tape over the dominant eye's lens,,, to make the less dominant eye do the work.
You can also learn to shoot with the less dominant hand.
Or, you can "cant" the gun to allow you to use the less dominant hand with the dominant eye.
But,,, even so,, you should TRY hard to shoot with both eyes open. I say this to help you become a better shooter.
You do not walk around with one eye closed,,, or drive a car with one eye closed, or any other activity. You have already "learned" how to do most other things with both eyes open,,, you have to work on treating shooting as any other activity.
There are world class action shooters with cross dominance,,, and they often use the Scotch tape method. It allows them to keep both eyes open, & see the entire stage & where they need to move in a "natural" way.