I am left eye dominate & right handed. I shoot from the right shoulder and close the left eye. This is no problem for rifle shooting. I have beenvery sucessfull at military rifle competitions in the past. The only time this will be a problem is when shooting with both eyes open (ie:shotguning). Ammittedly I am not the best with a shot gun but still use only one eye. If the rifle does not comfortablably come to the shoulder having a right handed person shoot from the left shoulder will only make the process worse.

Good Luck