I am left-eye-dominant, and have no trouble using an AR15 in lefty mode. Actually, in some ways, it is a better lefty rifle than rightie rifle. I am not actually right-handed overall, but it felt more natural to shoot long guns, primarily shotguns, in right-hand mode in the beginning. (I throw and kick rightie, and do small things lefty.) I started having trouble when I started using aperture sight and optics, however, and then found I was left-eye dominant. My switch to lefty rifle shooting solved that problem, and felt natural right away.
The only long guns that still feel natural to me right-handed are bead-sight pump shotguns.
I didn't start using the AR15 until rather late in life, after the infamous North Hollywood bank robbery and then 09-11-2001 convinced my PD's command staff to let us carry rifles. I started with an AR15A2 Govt Carbine, to which I added an ambidextrous selector and Norgon ambi mag release. I learned that neither accessory was necessary. My current AR, built around a BCM lightweight middy upper, just has the stock mag release, and the selector is the single-sided star-type from RRA. The AR15 really is a good lefty rifle. Brass ejection across
my right eye's vision? GOOD! I know that case got clear, and that is a sign that the next round is most likely good to go. Life is good!
Good things about running a duty AR15 lefty, and duty pistol rightie: the two weapons don't crash into each other, the sling won't foul on the holstered handgun so easily, and transitions are oh-so-seamless.
Think about it. If your strong arm is opposite you dominate eye, and you shoot from the shoulder corresponding to the dominate eye, it is your STRONGER arm that is doing the part of rifle shooting that actually requires the most physical strength.