ORIGINAL: dws
I used to shoot everything with both eyes open. But now that I'm older, I have to close my left eye to keep everything in focus. I would suggest using both eyes if you can, but if you can't, don't lose any sleep over it. There are more important things to good shooting such as anchor points and form and follow through.
I'm with cwoods shoot and dws. Give it a try and let us know. I think it's better with both eyes open. You may see something going on that you wouldn't if you were just looking through a peep.