I don't remember anything like that happening.
If there was backlash I think it was a vocal minority. Either way, the Lady Dynamite video isn't even a big deal. Ayu has always included sensitive themes in her career in a very tasteful way in my opinion. She never forces anything upon us or comes off as preachy.
I'd say the biggest blows to her career were Bold & Delicious/Pride, missunderstood covers, getting married/divorced, leaving Japan, and Party Queen.