Here's an interesting article on the topic that I happened to come across:
http://archive.fo/4mYgw
Basically, Steven Moffat correctly notes that there in fact is no major "backlash" against casting a woman as Doctor Who and advises the clickbait media to "shut the hell up" already about that canard, instead of trying to conjure one up to bravely combat. Clickbait media then portrays that as "harsh words" against the fictional backlash.
Oh, and Chris Hardwick once again makes a bid for his name to become a recognized expression in Cockney rhyming slang, to the same disingenuous tune.