The only way I can shoot at all is with both eyes open.
I'm right handed and right eye dominant, but I am monovision left eye corrected for distance. So I read with my right eye and see distance with the help of a contact in my left eye (going to get Lasik on my left eye this year). This can make shooting a bit of a challenge, but if I keep both eyes open I can sort of see the front sight and the target both.
For indoor range shooting I had a special pair of safety glasses made that corrects just my right eye, otherwise it's just too hard to see the target with the indoor lighting.