I think it's come down to how pejoratives are used to marginalize. Animals are not aware of the aspersions. But, pussy is definitely a sexist pejorative.

As to letting people push whatever opinions take their fancy regardless of facts, IME, no, they do not have a right to those opinions. That Sandy Hook denial further traumatized the survivors, surviving family, and that community. I think it's telling the courts agreed with the judgement against that cretinous nitwit, Alex Jones. Remember, Trump pushed his lies and conspiracy theories to an all out insurrection. And now, he is literally planning a full on dictatorship if he wins again. Free speech doesn't mean free of consequences. There has to be accountability for speech when it flat out lies and/or harms.