I see Waar's point on the matter of the Kirin. In order to be clear on this matter I looked up the description of a Kirin which is a translation from Qilin to Japanese and Korean.
Qilin from Wikipedia:
The earliest references to the Qilin are in the 5th century BC book Zuo Zhuan. The Qilin made appearances in a variety of subsequent Chinese works of history and fiction. At one point, however, it became identified with the giraffe, and even today, the giraffe is called a "kirin" in Korean and Japanese.
The Qilin became a stylised representation of the giraffe in Ming dynasty. It is known that on Zheng He's voyage to East Africa (landing, among other places, in modern-day Kenya), the fleet brought back two giraffes to Beijing. It is also known that these two giraffes were referred to as "Qilins". The Emperor proclaimed the giraffes magical creatures, whose capture signalled the greatness of his power.
The identification between the Qilin and the giraffe is supported by some attributes of the Qilin, including its vegetarian and quiet nature. Its reputed ability to "walk on grass without disturbing it" may be related to the giraffe's long legs. Also the Qilin is described as having antlers like a deer and scales like a dragon or fish; since the giraffe has horn-like "ossicones" on its head and a tessellated coat pattern that looks like scales it is easy to draw an analogy between the two creatures.
It is unlikely that giraffes and qilin were regarded as the same creature in pre-modern times however. For example, typical depictions of the qilin have much shorter necks than giraffes. However, the Chinese character 麒 and 麟 both carry Chinese radical 鹿, suggesting that it was originally a type of deer, or perhaps an antelope.
In a nutshell, Kirin is a mythical creature based off of a giraffe thought up by the Chinese. No mention of it having human features.
Picture of a Kirin:
If we are to argue that if lamias are okay while the kirin is not, it seems unfair, but lamias have human features while the kirin does not. Some may argue the kirin can turn into humans. In the descriptions I've read there were no mention of it turning into a human and if we allow this, that would mean anyone would be able to claim any animal or mythical beasts to be the waifus of a said fakku member.
Now that being said, I also see the point of the other members fighting for the right of the kirin being a canidate for a waifu since Horo, who is a wolf and can turn into a human (I've heard of stories of kirin turning into human) is a waifu.
But in the end, I have to say Horo is a special case and is a specific charcter. Unless the said member names a specific character, I don't think it should be allowed since anyone can waltz in and say "Hey I want a unicorn to be my waifu (just named any mythical beast off the top of my head)" which in the end just doesn't sit right with me.
That's my two cents but it's not word.