I gather Dawkins wears this kind of woke grievancing and cancelling and deplatforming as a badge of honour, like a man of intelligence and perception would. They look smaller, not he.

I haven’t heard this scandal.
It seems out of character, and he’s old, given the choice I would ask him to explain just what he meant. Perhaps he just said it wrong.
I’m not expecting him to be a transphobic apologist.
I’m trans and pissed off a bunch of gays by making a joke to a reporter when I was working to clean the sidewalks at Pride.
She grabbed me out of nowhere and said some big dollar amount that had been raised to help the LGBT cause, what do I think of the money raised?
I said if they raise enough they might find a cure.
We almost had a riot, with me saying Oh for fuck sake! It was a fucking joke! Jeez!

In 2015, Rachel Dolezal, a white chapter president of NAACP, was vilified for identifying as Black. Some men choose to identify as women, and some women choose to identify as men. You will be vilified if you deny that they literally are what they identify as.

He got cancelled. An award from 25 years ago was "taken" from him because what he said in a tweet was perceived to be transphobic. I don't know how much he really cares about the award.

The AHA apparently didn’t specify which comments they were offended by, so it is impossible to form an opinion. Dawkins is free to express his views, and the AHA is free to retract their awards.