I agree that a politician, like anybody else, is entitled to a private life and I do feel some sympathy for Vaz and his family.
However, I don't agree with Corbyn that this is purely a "private matter". Vaz is Chairman of the Home Affairs Select Committe which was conducting an inquiry into prostitution and making recommendations as to the laws relating to it. He has also talked publicly about the dangers of drug-taking, yet it appears he brought up the issue of "poppers" when he met the male escorts and seemed to have a fairly relaxed attitude towards drug taking. Some people feel that makes him unsuitable to have any say in discussions regarding the legal status of certain drugs.
There is also the issue that in effect he was leading a "double life" which presumably he would not wish to be disclosed to his wife and children or the general public. That being the case, would it not, had it been discovered by somebody else, have made him vulnerable to political pressure? Knowing this, I think he should have realised that he was not an appropriate person to be part of the Home Affairs Select Committee.
For those reasons, it's my opinion that his conduct is unacceptable and he should stand down.
I don't think there is any difference between a male and female prostitute but perhaps the words "rent boy" ("boy" in particular) conjure up visions of vulnerable young people being "rented out" against their will to predatory older men. Why isn't the term "rent girl" used - there have certainly been cases where under age girls are trafficked and forced into the sex industry, or vulnerable British girls are at first lured and then bullied into it.