Most of the meat we eat is wild game, I've guessed percentages before, but they're just guesses. I haven't bought beef more than once or twice in a few years now due to us having depredation permits on our farm.
Those deer (mostly deer) do get old from eating them day in and day out. I understand where some of the folks are coming from when they say they would rather buy the meat, but for us it's about protecting the farm and the cost of grocery store meat is so ridiculous that we couldn't afford to eat meat like we do otherwise.
After a few years of straight up deer meat, some good ol cow beef is pretty darn scrumptious!
We try to make the quickest kills possible, that does more for it than anything else. We do make sure to skin/clean them quickly! Next since I don't have proper facilities to hang the meat (certainly not going to pay to hang meat someplace) we do the cooler/ice method. I put the meat on something so it is up off the bottom of the cooler, empty water bottles work great. Layer Ice/meat/ice/meat like that at first so it will cool it off quickly, and then add more ice while keeping the drain open and the cooler tilted, this will get the blood out and the meat cool at the same time. How I clean them is different than most folks too. Since I don't have to travel with them, I can shoot and then start butchering almost instantly. I do not gut the animal until the very end. I'll remove ALL of the meat possible while keeping the insides intact, THEN I'll remove the insides and finish the job. Just a tiny bit of spilled urine can ruin a whole animal, and that is what alot of folks call 'gamey' it's actually urine. YES... I know how to clean one 'properly' but this works great and no worries about any spillage, if you do have an accident, you've already removed most of the meat so all you lose is just some of the belly/rib meat.
That said, I've only had a couple of does that I thought tasted like fine grade beef, these were killed well out of rut, shot with a headshot, and cleaned immediately. Bucks almost always have a bit more "gamey" to them...
The buttermilk thing does work, as does regular milk. As a plus, the lactic acid makes it a bit more tender as well... With a particularly 'gamey' piece of meat though, there isn't much that can be done. I've tried spicing it until it's just a ridiculous spice ball and you can still taste the gamey taste...
For most folks though, it's a psychological thing. After they've had a bad piece of wild meat, they'll always taste that.
Almost forgot... fat. remove every single bit of anything that isn't lean meat. Every bit of sinew and especially fat. Remove that little film that I can't remember the name of as well... I like to use a nice fillet knife for that. Every thing that isn't nice dark meat. It will make a MASSIVE difference. Even one little morsel of deer fat will put ALOT of game flavor into a whole dish. I personally don't mind it but as I said, I do get tired of it. Someone told me that once and when I remember to actually do it as I'm preparing a meal, I can certainly tell that I did. So can the missus
With a squirrel, not really doable, but with deer... heck yeah.