I had rabbit in the military mess hall. It was good. I think more people had a problem with the idea of eating rabbits than the taste itself. In Europe, you can often buy fresh rabbit meat on the open market. I think they have a different attitude towards rabbit meat, with a long history of eating rabbits as part of their diet.
When I was a kid, I hunted and cleaned some squirrels. We cooked them and ate them. It was not very good, but I mean we did not know anything about how to cook meat. No luck in getting mother to cook the squirrels, either. In my case, I decided it was too much effort for the amount of meat we got even if we could have learned how to cook them better.
I agree. My brother gave us some deer meat, venison, because he did like the "gamey" taste of the meat. I know my grandmother used to cook venison when I was growing up, and it always had the extra wild kick flavor to it. I was never a big fan of venison, but I ate everything grandma made.

Dear Wife, however, took the venison and made a salad of some kind out of it. No more gamey flavor and everyone loved it, even my brother who gave us the meat. So yes, I agree how you prepare and cook the meat does indeed dictate if it's going to taste gamey, or not.