The following is my take as a player, so read it as the gray it's written in:
Even though no one's stopping you from playing a character which in one way or another conflicts with or does not follow the Discovery lore and canon, it comes with the drawback that you can't "force" your character on others, and if your character happens to be a non-canon concept like a furry, people have the right to choose for themselves whether they want to acknowledge your character or not. Trying to force people to treat your character as they would treat a normal character is nothing but outright powergaming, as your character is in fact not a normal character.
Our server goes rather easy on non-canon characters, as there are no strict rules enforced against them, and admins have stepped in only in a very few occasions when that type of roleplay was pushed way too far. The official lore of the mod, however, has a more strict attitude toward the whole thing, so just because something is not hammered down on the spot by the server admins does not make it part of the official lore, and long as something is not acknowledged as part of the official lore, people have every right to treat it however they see fit, and based on nothing but their personal opinion of it.
For the sake of providing an example other than a furry character (even though that's most likely why you posted this thread anyways) - Take a a male character applying for a GC faction. It somewhat conflicts the lore of that faction, but neither the owner of that character nor leaders of that faction would receive a sanction if the character is accepted and starts flying with GC tag (there were, in fact, two male Chrysanthemums characters with extensive backgrounds. One was even part of the official [GC] back in the day), however, if the faction decides to deny the application on the sole basis of the character being male, the player has no right to complain, as he was going against the lore of the faction and the leaders of the group had every right to refuse to acknowledge it.