I didn't grow up eating game meat at all really. That doesn't mean I never had any, when we did it was usually venison from a neighbor right after the season ended.
We did eat lots of fish. I've been fishing for dinner since I was little. I feel like all the fish I've eaten are way more suspect than what I hunt now.
Only as an adult have I started to eat game that I hunted. Mostly because it's easier for me to hunt where I am now.
As to what I eat now:
Yes, to squirrel in the wild or near my house because I know what they are eating. They definitely are fatter and taste better during mast years when all the oaks around me produce acorns.
Rabbits, oh h$!! yes! I see it as insurance for my next years garden produce and they are truly delicious. We cook them a bunch of different ways but I love frying them like
Cowboy Kent Rollins does in the linked video.
Deer, again YES! I grow food just for the deer. I can't use an airgun to hunt them, so I need them in under 40yds to get them with my crossbow or the 100 year old Remington Model 17.
I've eaten lots of other "exotic" meats. My favorites have been ostrich, snapping turtle, and alligator.
I would try a rice rat in Vietnam just like I'd try a guinea pig in South America. It's all about context.