Some of us just ignore our left-eye dominance and train to work with it instead of training out of it. 😉 I don’t have much trouble with mine.
Kit @ Forevervain.com 
I am cursed with being a Left Eye Dominant, Right Handed shooter. To further confuse things, I shoot pistols Right Handed and rifles Left Handed. After getting back into the gentlemanly sport of firearms in 1999 and doing much research, I looked for guns with ejection paths that did not scare me. I found that although Benelli has Left Handed models available, their Right Handed semi-automatic shotguns worked just fine when shot Left Handed. I ended up with the predecessor to the “M2 Tactical”. I love the Glock for its K.I.S.S.  design (no confusing external safety levers) and have become a Glockaholic. Finally, my Bushmaster AR-15 (16”) is just so cute to shoot.
Today, seven years later, I am still satisfied with my choices. However, I am toying with the idea of getting a “true” Left Handed AR-15 design from Stag Arms in New Britain, Connecticut.  The downside is that their rifle uses proprietary parts that would not be available in a post SHTF scenario. But, Jim… I have this lust for one. LOL! Regards, – Doug S. in Connecticut
Stag Arms  makes a very nice left handed [variant of the] AR-15. My best friend has one and it shoots just as well as my right handed one. They are reasonably priced, too. – D.C.
JWR Replies: My guidance on the Stag Arms rifle is the same as that for any other firearm that uses unique or proprietary parts: Buy a lot of spare parts. And be certain that the spares are truly “drop in” replacements, that do not require hand fitting. Otherwise, you may end up with a useless ornament instead of a practical tool for post-TEOTWAWKI .