First of all, I want to highlight that I am aware about the feelings of this community regarding keeping track of friends/foes: in SO specific persons are not important, but questions/content.
I do agree with the aforementioned general idea. On the other hand, a too rigid interpretation of abstract statements might represent an obstacle to meet the intended goal.
I have certain personality and like certain things; equivalently to what happens with all the other users with whom I interact in SO. Being personal-opinion-independent does not mean denying that personal opinions exist, but understanding such a reality and properly addressing it.
What I am proposing here is to enable some kind of auto-tracking feature of past incidents with other users. Available-for-all-reps warnings helping potential contributors know what might be the best proceeding in the given situation, in order to avoid problems and deliver what SO expects.
I have an argument with user A while answering his question, as a result we both flag various comments and moderators need to intervene.
Two months later, I visit a question posted by user A (who might have changed his displayed name) and see a warning on the lines of "1 past incident with this user". With this information, I might decide to not participate in this question in order to avoid problems; or to proceed much more carefully; or even to write a nice comment on the lines of "Sorry about our previous problem. I hope you don't mind that I participate here".
Is this against a strict interpretation of “SO only cares about content”? Yes. But it is actually helping users overcome their personal opinions and deliver the expected objective on-topic behaviour, where only content should matter.
UPDATE (suggested by Emrakul)
Yesterday, I had an argument with a SO user, what has been the main reason for posting this proposal. I have got involved in equivalent situations quite a few times in the past (mainly over 1-year ago, when I decided to stop participating in SO for a quite long time; the main reason for this decision was precisely getting tired of being involved in this kind of nonsensical-to-me situations: off-topic discussions happening randomly). In most of the cases, the result has always been the same one: moderators deleting everything; and that person and me not wanting to deal with each other ever again.
Why would I (or anyone else) want to get involved in useless discussions? On the other hand, sometimes I had interacted with the given person later and realised that my previous behaviour wasn't too right (and apologised).
Just to make clear that I always try to be as objective as possible (in general, but mainly in SO). Most of my bad experiences in SO have precisely happened when dealing with not-objectivity-prone people (e.g., If I say something nice about you I would expect you to say something nice about me). The worst part is that there is nothing which either of us could do to change other's behaviour. So, why not helping to avoid so unfortunate (everyone loses including SO) situations?
Also note that I seriously think that my position is the easiest one and that, in this kind of incidents, I am the one losing less. On top of everything, I am currently starting a new stage in my SO participation, where I will be much less understanding with certain attitudes (e.g., stop talking to a person going against the SO objectivity-based expectations right away).