I don't know if this counts, as this is somewhat pre-emptive... I have an advertisement up for renting a room in my house on flatmates.com.au. In my ad, I say "women only". I still get the occasional man messaging me... and the occasional trans person. If it's a man, I politely point out the "women only" part of my ad, and it's no harm done.
Things are different though if it's a trans person though... sadly, I know from past experience how aggressive trans people can get (I've had death threats before) when told "no", and I'm scared of "pissing one off". I have to make up excuses as to why they can't come round and inspect my room... excuses that are very flimsy and would often easily fall down if the person at the other end was persistent.
I'm scared that if they realise I'm scared of them (this is literally what transphobia is) they will want to hurt me. And it would be very easy for them to find out where I live... alone, I might add... by asking one of their friends to apply instead.
Renting out a room shouldn't have to be a fearful process... or if it is, it should be within my rights to say "no" to anyone who is not of the same sex... it has become this way because I'm scared that if I say "no" to a trans person (or even admit that I'm scared) they will get violent.