I've been sorting out issues and getting used to my RMR on my Glock 17. I was having dot flickering problems, which I fixed by putting tape under the battery. I rezeroed it today. Previously, I zeroed it at 10 yards from the bench, with only my dominant eye. Doing this, I get perfect cowitness with the irons. I also two inches left at 10 yards. Shots that feel perfect go two inches left. Called fliers left go way left, and called fliers right would hit the bulls eye.

Today, I zeroed it again, this time with both eyes open, which I hadn't done because I have trouble focusing on the target at the poorly lit indoor range I go to. Now, I'm still shooting left, but all of my left shots are called fliers, and the rest hit dead center. However, my zero is different from before. The dot is now to the left of my irons when the irons are lined up. My dad has noticed the same thing on both rifle and pistol red dot optics. I've never heard of both eyes open shooting resulting in a zero change, but I am familiar with it both through personal experience and in the forms on ACOGs with BAC reticles. I'm curious if anyone else has had the same experience.

I have no idea why people think one eye needs to be closed.

Some people see 2 guns, or 2 targets

My wife's RMR looks to be to the right of the irons when I look through it. It's perfectly cowitnessed in a picture. Weird, idk. I never worried about it.

What you're experiencing is normal; it's an effect of Stereoscopic Vision (aka we have two eyes spaced a couple of inches apart; it's what gives us depth perception).

With red dot sights, regardless of whether it's on a handgun or rifle, the shooter is supposed to keep both eyes open and focus on the target.  

Ultimately, zero it using the method with which you most often shoot.  If you're upset the dot isn't nestled perfectly atop your front blade, drift the rear to line up.

I'm not sure if I'm reading this correctly (the underlined sentences in the 1st paragraph are confusing).

Are you saying that with one eye open you first zeroed the standard sights on the gun and they shoot to POA with the irons ONLY. Then put the RMR on the gun, cowitnessed to the irons and it shoots 2" left?

If the irons on the Glock are adjustable (not a Glock guy), you may need to rezero both after mounting the RMR. This is not an uncommon phenomenon with RDS/Holographic sights on rifles. Irons are zeroed, add Aimpoint/Eotech, BUIS POA no longer = POI when seen through the optic. You need to zero the optic, then rezero the irons while sighting through the optic.

The purpose on carbines is if the optic goes down (battery failure or whatever), you can immediately transition to using the BUIS by looking through the optic without needing to remove it first. On combat carbines there are 2 differing opinions on this part though.

If the glass in the optic is damaged to the point you can't even see the front sight through the optic and need to remove it, the BUIS that were zeroed looking through the optic may be off when the optic is removed.

Some folks prefer cowitnessing through the optic and testing deviation with the optic removed, others advocate zeroing the BUIS without the optic and leaving as-is after mounting the optic and dealing with any deviation when viewed through the optic (the POA/POI change for the BUIS after adding the optic is not a given. Happens with some, doesn't happen with others).

The 2nd issue of the POA/POI changing when shooting both eyes open vs one eye open is a separate issue and can be trained out.

It's due to your brain switching eye dominance.

If the optic has been properly zeroed so POA=POI, it should be accurate when you aim through it with either eye (eg. Shooting strong side vs weak side).

If you're shooting right eye only (left eye closed) and hitting accurately after you've got a good zero, then find your POI is off when you shoot both eyes open, it's because your brain switched to dominant focus with the left eye. Your right eye is now only superimposing the red dot on the left eye's view. The difference in viewpoints between left vs right eye causes the deviation.

This happens when the eye looking through the optic is (consciously or subconsciously) unused to the sight picture because it's noticeably different from your normal view with the unaided eye (eg. common with magnified optics like ACOGs, or if the optic has a noticeably dimmer view, strong tint, folks unused to smaller apertures etc.).

You can train to force yourself to focus primarily with the dominant eye, using the other eye for peripheral vision/awareness. Some folks find this adaptation easier than others.

If I shoot w/ both eyes open on a red dot, I'm lucky to hit a barn door.  The triangle test shows I'm right eye dominant, but the target says otherwise if I have both eyes open.

I have been shooting both eyes open since I have been shooting( my dad the marine)... I have also taught my kids to shoot both eyes open, my daughter however just since her late teens has been having the same issues as stated in OP.. she also sees two of everything now compared to when she was younger.  Dominant eye shooting with both eyes open is natural but not easily obtained without practice. eventually muscle memory takes over and your dominant eye will focus on your dot/front sight...

Interesting.  I'll have to remember to try it the next time I take the P07 or P09 to the range.