The major source of conflict in the community is between those who want the game played in Open and those who wish to play in solo/pg, between those who want to play the game in a dynanmic, emergent, and spontaneous manner and those who wish to be anti social and play segregated. Its always been the case but ultimately the responsibility here sits with FD. It is their system by design and its problematic.
With that said historically I think you'll find that much of the hate, anger and spite has come from the PvE collective. I have simply lost count of the number of threads crying griefer and using pejorative terms to label one style of play. That by the way is apparently acceptable on this board. So there is a deep sense of injustice felt because I think its fair to say the narrative allowed here is biased to a certain extent.
Over time I think people got sick to death of being maligned and negatively characterised and have started to argue back. Its somewhat amusing to me that after being called all the names under the sun players who like a bit of PvP get instantly hammered if they counter 'griefer' with 'carebear'. Believe me there are a lot worse terms that could be used.
I'd be more than happy to not use pejorative terms myself and I'll do that the moment I stop hearing people wail about 'griefers'. Needless to say I won't hold my breath.
As for the community I think in general despite the conflict its not a bad one. Particuarly demonstrated in the way almost everyone jumps to help out new players and offer advice. So its not the picture you paint and my advice in general would be for people to chill out a little, and lighten up over these percieved offenses. At the end of the day its just a bit of fun. So what if a few people have their ships blown up. Its not the end of the world in a galaxy set against a backdrop of raw anarchy and power plays, is it?
I think you misunderstood the term "antisocial behaviour" here. A player who plays without any interaction with other players, who plays against environment only, maybe even only in Solo, can not, by definition, be antisocial. They may be asocial, which is a very different thing and means they do not wish any social interaction and prefer solitary gameplay. They may also simply prefer solitary gameplay and their preference may have nothing to do with disliking society or social interaction.
Antisocial is a person who's activities focus on harassing others and breaking the norms of society, or in this case, a gaming community. Again, by definition, being antisocial requires other members of society to be addressees of such a behaviour, either directly, or indirectly. So again, by definition one has to PVP to be antisocial.
As for the term "griefer" it is not a friendly description, but it is used, or should be used, to describe rather unfriendly players who display antisocial behaviour in multiplayer games and in this case this is not a derogatory term. This term should not be used to describe players who simply enjoy PVP gameplay as it's perfectly possible to play PVP game and not be a "griefer". If used in such case, this term becomes derogatory.
A term "carebear" is used much more indiscriminately and typically applied to all players who have preference for PVE gameplay, by players who have preference for PVP gameplay. That's why it is derogatory. Hope you can notice the difference here.
This is not to say that PVP gameplay is antisocial per se as there is nothing wrong about PVP and it's permitted by the rules of the game. I am also entirely sure that no player playing in Open, who is in their right mind, will be opposed to PVP gameplay for as long as it is within reason. Every player can be attacked in Open and I'm sure many players play in Open precisely because of that, because they enjoy PVP element of the gameplay. Problems appear when some other player harasses them repeatedly for no ingame reason, or is a coward (unprovoked Conda on a Sidey attack is cowardice for example) or is cheating (unprovoked Conda on a Sidey attack is cheating, for example and so is combat logging).
"Dynamic, emergent and spontaneous manner" versus "antisocial, segregated"... I have a hunch you may be pushing some agenda here, you know? It's fine that you have your personal preference for one or another gameplay style and it's rather clear here, but the suggestion of Solo / PG being somehow less "dynamic, emergent and spontaneous" is not exactly the heights of diplomacy. And that is what causes conflicts in Elite community, not the presence of various modes of gameplay.
There is absolutely no conflict caused by the fact that people can play in Solo and in Open. These are two game modes that are absolutely valid and part of the gameplay. They cater to different play styles and that's it.
Your advice for people to chill out a bit is a good one, I wholeheartedly approve of it.
I would add one bit of advice to people who enjoy PVP: have some dignity and keep PVP meaningful, look for some challenging targets and make sure you don't harass people repeatedly (as in: don't blow up the same ships over and over again unless their pilots are clear they are interested in PVP). And don't interfere with gentlemen' agreements of private groups. And everybody will be happy. Here, conflicts within the communities sorted.