Badly; very very badly. ^^; I actually made a topic about this issue some years ago on this forum, and since then I think I've gotten worse instead of better...which is why my policy is usually silence. =P If it makes me mad when I read it, I take it out of my feed and move on, and hopefully maybe someday I'll read it again in the future when I'm less irritable.
Of course, normally the course of events DOESN'T end up being "oh, this person had some valid points, I'm glad I took some time to cool down and consider their opinion".
Normally it's "wow, this person is an ignorant fool; I'm glad I didn't respond to them 'cause they didn't deserve it".
From the outside looking in, it probably seems * suspect * that most of my negative feedback comes from bigots and clowns (ergo it just happens to be morally correct for me to ignore all my critics), but I swear it's the truth. O_O I'm just that unlucky.
Recently "I'm going to head-canon your characters as the correct gender, just fyi" has become a thing that is okay to say to me apparently...I think I'd actually be really happy if someone came to me with a criticism that wasn't completely selfish and/or useless to my work.
I kinda disagree with the 'Rude Expert' panel-- sure, someone who's mean to you can certainly have a valid point, but you don't have to give them any consideration, not even 'begrudgingly', if they clearly weren't willing to give any consideration to you.
Being able to convey thoughts and opinions without berating/insulting people should ALSO be part of becoming an 'expert' in your field, and I think this idea that people who are 'talented' or 'superior' are no longer beholden to lowly things like common decency causes a lot of problems in all spheres of criticism. If they're so great, we should be holding them to a higher standard, especially when they're punching down at younger, less-experienced artists.
If the best mangaka/cartoonist/animator in the world wrote a nasty callout post about my work, and I decided to just insta-block them and pretend they never said anything, I think I would be totally justified in doing that, and I would feel ZERO guilt about whether or not they "might have a point".