You are thinking too narrowly. Think broader. When Pelosi's husband got attacked by a crazy dude with a hammer, there was definitely a level of glibness from the right, including from the Late C Kirk. When Democrat Senator John Hoffman and Rep Meliisa Hortman were shot, there was also a large degree of ambivalence at best, gloating at worst. It really all boils down to what your personal values are, and what your algorithm feeds you about the other side. If you aren't a liberal, you probably aren't getting news stories about bad things republicans do, You're getting storing about lefty retard tranny commies addicted to abortions and black tar heroin. By that same token, a liberal isn't learning about the latest out of touch moment from their party, they are getting flooded with stories about conservatives being malevolent shit eating fascists addicted to fag drags and removing human rights from minorities.
So yeah, you probably haven't seen much conservatives being assholes online, but that's probably because you are a) not looking for it, b) agree with them that the other side is cartoonish bad, or c) the news that is fed to you has not shown you the information on purpose. This also applies to people on the left, and is why the divide is growing larger and larger while only benefiting "news" grifters, who profit off our attention and fears. Politics on a whole has become a mean, ugly, and stupid place, and I do not see the genie going back into the bottle anytime soon.