As for the npc in the training room, the problem isn't that they put a furry in there, the problem is that Skullgirls suffers from the worst case of "it's an obscure videogame reference, you wouldn't get it" syndrome. They cut together a bunch of shit from other games to make the characters and backgrounds, and put references to other stuff goddamn everywhere. There's not a single original idea in the game, neither graphically or gameplay wise.
I mean I dig the game, but you have Peacock with a touhou colour scheme, Ms Fortune with a Pussycat one (from the claymation), there's an entire Lovecraft Town (Little Innsmouth, populated by fish people), and Zone-tan is an NPC in the game too (yes, I know they got Zone working as a background artist, but that doesn't excuse it).
Referencing stuff constantly like that is the lowest form of writing, it means the creator does not have a single original idea and he is just snipping together shout-outs to other creators. You can use all those inspirations without making it obvious that you are referencing something, but the game isn't doing that, the game is straight up BUILDING itself up from blatant references and artist OCs.
So in that vein, putting in some gaylords fursona in the background blends perfectly with the games design. Problem is that the game had shitty design from inception. As stupid Indivisible is, at least they are making something slightly more original there.