It boils down to your stance on the whole "be tolerant of everyone but the intolerant" issue.
Well sure, we can reframe the conversation and have the same discussion using that framework.
But in this case, dehumanizing would be "intolerant of people or groups" whereas being intolerant of their ideas and their expressions of those ideas may not be dehumanizing.
The difference is put quite well in @Celtz's situation. Whether she got through to the woman or not, she recognized that she was human and worthy of a response.
You don't do that to a mosquito - if it bites your child you react with violence, exclusion, or some other method to prevent the situation from happening. You certainly don't try to reason with it or change its mind.
Does that mean I think all racists, all prejudiced people, all anti-gay people, deserve to be killed, should be shot, deserve to be beaten? No, it definitely does not.
This, however, is the extreme view, and the question is whether those people deserve human rights - the right to express themselves, for instance.
But an even further, and more difficult question is this - do they deserve to be treated with human dignity and respect? Do we immediately go to shunning and exclusion, or do we attempt to have a discussion with them, with the hope that they might change, or the hope that we can better understand them? Can we possibly have compassion for them as human beings, or when they are harmed do we allow ourselves to be glad, or possibly celebrate the injury or death?
Because one thing I've learned is that if you refuse to see the "other" as human, and choose not to associate with them, they will never move towards you, and in fact may become even more fanatic in their beliefs.
But this compassion, this belief in basic human rights and dignity, must come from within, and be reflected in all our actions and speech. We can't post here where our audience is small and deride one group or another, and then believe that in public we treat all humans equally and give them the respect due any human.