Regardless of the sight type, I shoot with both eye open, which is how I was taught by my father and grandfather. As pointed out earlier, it increases your field of view and reduces eye fatigue. It also helps maintain depth perception.

Sometimes I shoot left handed and with a bit of concentration, I can shoot both eyes open from my non-dominant side. Mental fatigue kicks in quicker when I do. At the archery shop I used to hang out as a kid, the owner used to have me shoot the left handed bows he tuned for customers to make sure they were set up and shooting right.

I find it easier to use an RDS shooting left handed than iron sights