I used to play pool at a high level in my 20s. Similar situation there. My dad was also one of those odd ones that did some things lefty some things righty. There are pros that are definitely cross dominant with their eyes and play amazing, although their lineups might be different. Usually though for shooting sports you want to line up along your dominant eye. For baseball, it's an advantage to be cross dominant because your dominant eye ends up closer to the mound to pick up the pitch. I believe it's a lot more common to be left handed and right eye dominant than right handed and left eye dominant. For throwing a football, I'm not sure it would matter much.