I'm mostly right handed. I write and throw right handed. I've been shooting lefty since I was little. I am left eye dominant, and managed to figure that out before I even knew what that was. The only odd thing, is that I feel more comfortable shooting a bow right handed. Most guns I've shot have been right handed. About the only problem I've ever had was some lever actions that liked to toss brass into the bend in my elbow. I've never had anything hit me in the face, or go down my shirt. I don't know how many tens of thousands of rounds of 12 gauge I have shot through a right handed pump action, and I can't recall ever being touched by an ejected hull. My least favorite type was always a bolt action. One day a steal came up for a Savage 110L, and I really like that rifle, but I'm not at all impressed by the bolt being on the left.
I've come to the conclusion that in cartridge guns, shooting a right handed gun, left handed, is actually an advantage! The loading port is right there. Lefty's have a clear advantage to port loading guns. The one and only disadvantage I have ever found to a guns direction is the safety. That's why I really love guns like the Mossberg 500, Savage 110, and the M14. A perfectly centered safety is the ideal situation, no matter if you are right or left handed. The tiny, tucked up behind the trigger guard button like Remington often used is the worst.
As for muzzleloaders, I've only tried percussion left handed. I didn't like it, as I had to swap everything to cap it. When I chose a kit for my flintlock, I barely had to think, and stayed with a right handed. The pan is right there in front of you, if anything a right handed flintlock should be easier to handle as a left hander. The only thing I ever heard was that now the flame is closer to your face. I didn't shoot my right handed TC Renegade flintlock that much, but I couldn't tell any difference whether I was shooting it off my right or left shoulder.