Both eyes open and you can train your dominant eye to become stronger or at least to the point where your focus is directed. Either way, both eyes open is the way to go.
In my experience (including my personal experience) it is simply not possible for everyone to train themselves to shoot with both eyes open.
Ocular dominance varies. Some folks have a very dominant eye, and it is easy for them to line up sights with that eye with both eyes open. Some are co-dominant or nearly so, and they will always (especially, we may assume, in an emergency) see two sets of rear sights and two targets when focusing on the front sight (or two sets of rear and front sights when focusing at the threat).
There are people in the middle of these extremes, and I think some can train themselves into using one eye for sighting with both eyes open; again, how dependable that might be in an emergency (with bad lighting) is open to question (unless they have done low-light competition shooting; do such competitions exist?).
The hopelessly co-dominant (like me) can train to briefly close the non-sighting eye to confirm a flash sight picture before firing; the eye opens again after the shot.
There are trade-offs, but losing 30 degrees of peripheral vision for less than a second (during a time when, because of stress-induced "tunnel vision", you shouldn't be depending on peripheral vision anyway) is probably the better option compared to firing with your sights misaligned because of visual confusion.
the doc just changed one eye so I can read without reading glasses.
The industry term is "monovision": one eye corrected for distance, one for reading. I have a pair of monovision shooting glasses: my sighting eye is focused
at the front sight (not at reading distance, more like computer distance), and the other at distance. It helps.
But it's unlikely that I'll be wearing my shooting glasses if I'm attacked.