Even if you couldn't include that sort of stuff in listings, there are still slumlords who will decline anyone who doesn't match who they want. The moment they heard an accent (or lack-thereof) or just read a name in an e-mail, they could just pass over the applicant. It's not much different than a racist manager denying anyone who isn't, say, white or Asian from being hired. All they have to do is say "thanks, we'll contact you in the near future if we feel you're a good fit!" but then never contact them.
This sort of thing isn't new, sadly. It's "silent" prejudicsm.
This sort of thing isn't new, sadly. It's "silent" prejudicsm.