You should turn off your anon thing and then see if anyone messages. Which I highly doubt because without the use of being anonymous, no one will make rude comments.
Really, people who send anonymous hate on Tumblr are often better left ignored. Many of them are only looking to see people get angry at them so by getting angry of the anonymous hate messages, you're giving them exactly what they want. It's just better to delete the anonymous hate and not address it at all.