I'm saying by your logic surely it shouldn't matter either way. If people shouldn't care that he's male, surely they also shouldn't care if the doctor is female?
I just think people are trying to force diversity too much in media and doctor who is just one of many examples. There was a petition for frozen 2 for Elsa to have a girlfriend. I'm not saying diversity is bad but when it's forced and put in due to pressure it doesn't work.
This sexist thing seems o be going way out of hand I guess. I'm okay with everything but if the original character was a guy, please let it be so. You can make a Batwoman but please don't try and experiment with some of the key traits, Dr. Who's gender in this case. I guess if they are intending a spin-off or an alternate universe kinda thing, then I guess it's okay, but I personally don't like things experimented only to please right activists. You can have all the rights you want, but please, don't doubt the genuine intentions of people who vote for a male Dr. Who. Everyone isn't a sexist.
Short answer.. No
As long as they can act well...who cares really?