Removed my previous comment because it had many mistakes that bothered me, and because I can't edit comments on this site after 10 minutes or something like that, so I had to make a new one.

Assuming your "hypothesis" is true, the next step in getting at the underlying causes is to ask whether these species are liked because they are popular, or popular because they are liked, mostly for their appearance. You seem to mostly imply the former, but I think that is a combination. This might be testable in that, the more it is the case that popularity comes from emotional appeal of the species instead of popularity itself self-perpetuating, the more there will be alignment between what furries like and what general culture likes, because the latter strongly optimizes for what people viscerally like. Your examples (foxes, lions, wolves, candids in general) seem to me to support such an alignment, though obviously it's a matter of degree. (That assumes that there's not some flipped switch that draws people to like anthro animals, in which case what furries like may be different from other people. The other option - ignoring the social factors etc. that cause people to become furries - is that it is a difference of degree and not of type.)

(I would be interested to know what the differences are in non-memetic appeal now, where most people hardly ever encounter wildlife, and back when our selection of species (which seems to roughly correspond to what you might find in the vicinity of a farm in medieval Western Europe) was produced, when people did. For instance, I hear a lot about how candids are "traditionally" "tricksters" in various cultures (although accounts of this are coming from popular sources and so are being filtered to agree with me), but this seems to have declined recently, which seems to me to imply that people are now getting their idea of candid behavior from domestic dogs rather than e.g. foxes. More broadly, I predict a recent rise in a system where popularity is determined be appearance, instead of behavior, except in the cases of those animals such as dogs that people still have regular contact with.)

If you're saying humanity is more likely to sympathize with canids or felines... Uhm... yeah, we kind of domesticated those two critters.

Why aren't people more sympathetic to apes (personally I found Johnny by far the most likable character in that movie, but he was voiced by Egerton, who I love) probably has something to do with the inverse. Humans are unnerved by animals that are so close to humans. Humans tend to like creatures who are adaptable and affectionate, but also not so smart anyone feels threatened. Also why I think elephants don't get as much affectionate.

Now, on a personal level, while I use a wolf as my main avatar, I have nothing but appreciation for every animal under the sun. I also find it frustrating how the furry fandom is sooooooo cookie cutter. People tend to push painfully generic stuff.

I totally agree with your hypothesis, but that is the duty of real creators: to push new and interesting ideas.