We are referring to humans on a continuum of an abstract concept called 'gender.' What it means to be a 'woman' or a 'man' or a 'eunuch' have changed radically over history - there have been female kings and male queens, 'two spirit' people who didn't fit into their society's division of male and female, stories of women as men to go to war.
The division between a man as an object, an animal, or an abstract concept are far deeper and more meaningful Also, vanishingly few people actually do ask to be referred to in inhuman terms, unlike trans* people who represent a small but significant minority.
But let's take one subgroup who might be asked to be referred to as inhumans - furries. If we took a furry seriously in their choice of animalit would put responsibilities on us to treat them as such (a wolf, for instance, would be captured and either kept in captivity or released into protected areas - or shot.) as treating them as their animal personalities would mean excemption from human justice (if we treated a wolf furry as a wolf and they killed, would we put them down like we would to physiological wolves?) Treating a furry seriously places unnecessary duties and responibilities on society which doesn't apply to treating a trans* woman as a female.
The only time when demands are placed on society is segregated areas for toilets/ changing areas/ etc, and here it's worth noting that trans* people are frequently abused, beaten or even killed for not conforming to other people's ideas of their gender and for most trans* people, a visit to a public bathroom or changing room can be a truly nerve-wracking experience. On the basis of doing the least harm, perhaps society can make this small accomodation?
The only other time is, I suppose, in sport. Frankly, I have so little interest in sport that I'm not going to bother making the argument since it hasn't come up in about 5 pages of discussion. As far as I'm concerned it's the only serious area in society where there might be grounds for discrimination.