Doubtfire and Tootsie triggering backlash is a case of correlation but not causation. As Ermengarde mentioned, the backlash to both was confined to a niche segment of theater people on social media. Tootsie was flailing from the get-go; its score was Yazbek cashing a check and Santino Fontana was never able to gather momentum as a star, must-see performance. Doubtfire is pretty much in the same place- mixed reviews, humdrum material, and no "must see" chatter around Rob McClure. Both of those properties are based on films with beloved star turns from recent memory- the musical adaptations lacked them entirely, and lived in the shadows of their source material. If anything, the two shows demonstrate that the "put a recognizable title onstage" school of producing is the failure here, not the content of the material.
"...everyone finally shut up, and the audience could enjoy the beginning of the Anatevka Pogram in peace."