I shoot with both eyes open. I am an NRA instructor and the NRA advises to use 2 eyes as well. At first it'l be tough to use both eyes, because you may see double vision when looking at the front site. This will go away however the longer you use this method. I shoot like this because I believe you have better vision overall.
If the time comes when I need to use the pistol for self defense, studies show the body will not allow us to close one eye in that situation. So, I practice for that.
I even shoot bullseye with 2 eyes open....