While I don't know how other MMOs handled this particular conundrum (if that conundrum even exists), a problem with adding beastial races to FFXIV is that the game has a pretty clear division between the "player races" and the "beastman races". There's a reason why Ixali can refer to a player as "smoothskin" and for it to make sense regardless of what race they are! If true furries were added to the game, there'd have to be a reason why they're not just considered to be another variety of beastman.

That's the biggest reason why I doubt we'll ever see a furry race in FFXIV. Just humans with variants of size, limb proportions, and animal bits.