Why should it matter if an otherwise good answer came from an LLM? Presumably no one is bothered if a human author is aided by a search engine, tech blogs, their own intuition and experimentation, or some guesswork - so long as they submit a quality answer; so why should it be any different for answers aided by LLMs - are they supposed to be automatically worse?
The sole determinate of whether an answer should be allowed is its quality (i.e. usefulness to people accessing the site who are trying to solve their programming problems). An answer's origins are irrelevant (except for the purpose of attribution).
StackOverflow's voting system already does an excellent job of getting the best answers to the top and down-voted ones to the bottom. Further, high-rep users have the ability to close/delete very bad answers.
Protesting LLMs seems like not much more of an extension on the idea of protesting autocorrect.