I'll never claim that nobody out there is opposed to changing the race, gender, or sexual orientation of a character is in opposition simply out of bigotry. Whenever you say, "Nobody is saying..." you end up getting burned.
Just don't claim that every gripe comes from bigotry or that ratings dropping is solely due to bigotry.
The problem isn't with having a bisexual Robin. There have been a lot of Robins since Dick Grayson. You can make a new Robin and make him bisexual. The problem is suddenly saying that Tim Drake, who has been around for 31 years, is bisexual. George Takei had the same problem with Star Trek: Beyond making Sulu gay. I can't imagine any of my SJW friends accusing Takei of being homophobic; but, Takei said in no uncertain terms that he is gay and his character wasn't.
No, Dr. Who isn't losing viewers entirely due to sexism because they cast a woman. Dr. Who is a good example of a situation where it's easy to justify a race or gender or sexual orientation swap. The first problem is that they cast a woman with the charisma of a wet blanket. The second problem that I'm seeing, and I'm speaking only for myself, every hardcore Whovian I know is a woman. Maybe David Tennant and Matt Smith were bigger draws for that audience?
The bigger problem though is that when these swaps are happening now, at this point in history, the swap is becoming a club that the authors are using the beat audiences over the head. The message is more important than writing a character and a story.
People want be entertained. People go to church or the internet to be preached to.
What's worse is this odd idea that we should put race, gender, and sexual identity the defining aspect of a character. I understand the overcorrections happen; but, we should understand that we're dealing with a overcorrection right now. Yes, represent people and do it honestly; but, don't make race, gender, and who the character wants to have sex with what defines the character. When you do that, we're not even seeing a character - we're only seeing a projection of a person's perception of what a certain group is supposed to be.