[Tuukka]

Just my personal experience, I am left handed, right eye dominant.

I shoot both short and long weapons left handed.

Shooting SMGs/rifles ( and pistols ) both eyes open has not been an issue, atleast I have not seen it as something that would hinder my performance with long guns, either with iron sights or red dot / variable power scopes.

In the Army I shot well in the range quals and due to my civilian shooting background, our instructor was pushing me for a slot in the sniper NCO course, but I declined that offer to go to a another unit. Also shot well in our applied training shoots later on.

I shoot both pistol and rifle IPSC at a national level, ie. I was on our national IPSC Open class rifle team between 2009-2012 and I am now in the Production class national pistol team.

Like said above, have not noticed any limitation to my performance from cross eye dominance.