When it comes to disability, I might refuse someone whose disability would cause risk in using the apartment and might have an accident because the apartment is not safe for someone who's disabled (the building is 300 years old, there's no elevator, the stair in the duplex apartment doesn't have handrails)... It's a risk if the person then has an accident...
Similarly in term of age, I would not rent to couples with young children because it's too risky.
So, it's discrimination but it's mostly because this is not an hotel, it's an apartment in which I live part of the year and it's not adapted for disabled people or couples with young children because I'm not in those categories.
That said, as someone whose wife is asian, I fully understand the problem. It's annoying and painful when people discriminate based on race.
In our case, we show both my face and wife face on our Airbnb profile photo because we prefer to have a host refuse on the basis of wife's nationality than to give money or stay at the house of a racist host. I've had a bad experience before that with a host who was nice to me when I met him and then wasn't as nice 5 minutes later once my wife arrived... The fact that he earned money from our stay galls me...