For better or worse, a highly-public character puts a writer into the spotlight, so every statement is looked at and scrutinized, particularly when divisive or unpopular decisions are made with that character. We still revisit and breakdown statements from leadership and writers about Clone Saga and One More Day decades later.
But I think you're right that as a result there can be a Streisand Effect by harping on every low-outreach critic with a chip on their shoulder towards your writing. It just boosts their profile and their criticisms. That hardly means to roll over, and I don't envy creators trying to defend their integrity or pushback on misleading claims, but there does come a point where you accept the internet is the internet and, ultimately, who are you trying to reach and who are you trying to convince? If someone has made up their mind already, it's just wasting time and effort that could be spent on better, more productive things.
I wish I could recall which creator said it, but he basically opted for a more positive outlook on the discussion, saying something along the lines of "they want a great product and this is the only way they know how to express it". Most people are not well-articulated, well-spoken, even-tempered, logical beings. Many want something good, and others are just trolls, and it takes wisdom to discern which voices to listen to and which to ignore or block.