Because some of us had some bad experiences with some specific users on other sites in the past, it might help if there was a way to mark posts of specific users, so it might be easier to ignore them or to live with them in peace.
The more drastic approach would be to hide every post of such users, but since the aim of this site is to serve not only as a community but as a repository of knowledge for future visitors, this will be contraproductive.
To me this is an X-Y problem.
I feel the site rules should foster an environment in which this situation doesn't occur - we're here to curate content not argue with each other.
I feel it's important to remember the target users of the sites - professionals and experts. A set of rules around engagement (i.e. be kind) should be enough, with moderation for individual breaches of those rules. We can't look to constrain behaviour *too* much - this is where SE failed for me. In this respect as Caleb mentions, we should focus on content, not people.
I would give a high level of personal ownership to the decisions made by the moderation team, but ensure the userbase within each site has the ability to flag and deal with systemic moderation issues via some democratic process.
If the flagging process works correctly, this situation should be dealt with quickly anyway.
I think this suggestion is picking up the snake from the wrong end. The site interface should neither promote nor demote content based soley on the user who posted it. If *we* as participants can't step away and ignore a user we don't like, no amount of tooling is going to completely solve this problem[^1]. Sure the tooling can make it a bit easier, but I think the first line of defense is to not put too much focus on the individual(s) involved in the first place. Keep the focus on the content. Interact with the content first, and lets not build to many tools that focus on the personalities.
Given the high visibility of chat pings, it might make sense to add a "mute" feature. I would first make this a per-room (that is, per question thread) mute. Sometimes discussions get going and it isn't just one user that's a problem, you just want to stay out of the whole conversation. That should be the first step.
Secondarily muting all pings / notifications generated by a specific user might be a reasonable step. I don't think hiding the content is a good idea at all given the way all content is at least somewhat interdependent. Posts would all display as usual, voting would be as usual, but the "comment" link as well as any avatar links that would normally ping the user would be disabled for anybody you had on a mute list, and no actions of that user would generate notifications for you.
Only as a last resort, adding the ability to hide chat messages entirely (again not posts, only chat messages) from the active room and (not transcripts).
If there is still a problem at that point then moderators should step in. If multiple people on a site are ignoring the same user, that should come to the attention of somebody with some moderator priviledges and some kind of warning system. What that system looks like should be discussied elsewhere, perhaps [on this question about moderator tools](https://topanswers.xyz/meta?q=182).
[^1]: Incidentally I think this issue is a large factor in where SE jumped the shark. Trying to blame only one end of an interaction for the friction is a loosing battle, both parties have to have some culpability. Rather than complaining about others and trying to legistlate what they can and can't say, we have to realize people are going to disagree with us and have that be okay. Sometimes people are [wrong on the internet](https://www.xkcd.com/386/) and you just have to let them be wrong and go to bed.