To be fair, that argument is really stupid when applied to The Doctor. The Doctor is not just a new actor playing the same character. It's an alien that creates a brand new body for itself every time it's old one is killed. And it's never established that the new body has to be the same gender as the old one. And in fact other members of The Doctor's race have already done this, so it has been expressly established that this could totally happen.
So for anyone that actually knows and cares about the show and the character, there's literally no reason this doesn't make complete sense. So anyone complaining about this change comes off as someone who doesn't know anything about the show, and if they don't know anything about the show, the only reason they have to be complaining about it is because they thought it was an excuse to complain about men characters becoming women. Which makes them look like a right-wing woman hater.