When I was in basic training there were several people that were right handed and left eye dominant. They made them shoot left handed. I noticed because I am left handed. They always called us out to give us brass deflectors. Those guys all shot better left handed than right handed.
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Generally having left eye dominant and right handed shooting a rifle does not affect that much unless psychological. The reason is that when shooting a rifle with your non dominant eye the sight radius is long enough to correct most issues shooting right handed with the non dominant eye. With a pistol it makes a word of difference due to the short sight radius. And will not work at all. When shooting the rifle just practice closing your left eye. If you practice enough you will see improvement due to becoming more confident. Or as stated you could switch and start shooting left side left eye dominant. My younger son is left eye dominant and right handed. He finally swithced to shooting a rifle left handed and became "more than proficient" after some work. But just could not addapt to shooting right handed being left eye dominant. Good Luck! Or get a good optic for your AR! This will also solve the problem. EOTech, Pro Point or other good sight with no parallax.
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Today, we need a nation of Minutemen, citizens who are not only prepared to take arms, but citizens who regard the preservation of freedom as the basic purpose of their daily life and who are willing to consciously work and sacrifice for that freedom."
When I train, I always spend part of the session switching from strong side (right side for me) and support side (left for me). At first, it was really awkward. Now I can shoot about as well support side as strong side.