Not the OP, but I'm in the US and.. it's complicated. I would say, in general, meats like lamb and, especially, veal have fallen out of favor due to the perceived poor conditions and youth of the animals. Rabbit isn't common in the US (it's not generally available in stores) but the "cuteness" factor plays a role here as well. This has changed since the 80's when lamb and veal were more popularly consumed. I'm guessing PETA's work has moved the needle in this area.

Living in Minnesota, however, wild game is more widely consumed so things like duck, geese, pheasant, etc. aren't seen as odd or offensive.

Horse is considered taboo for consumption in the US.

I would say, in general, Americans can be turned off a meat source if it is perceived to have produced from poor conditions or is "cute". This, however, does not apply to beef, chicken, or pork. (Though you can squeeze a few more bucks out of people by calling something "free range").