So, they stop inviting me to play with them. But why? It wasn't me, It was my character!
Probably because you were playing a cooperative game where all the PCs were members of the same party. Some PC vs. PC hostility, even the occasional violent confrontation, might be expected, tolerated, but characters that are not compatible with each other won't make for a sustainable party dynamic.
The ED equivalent to a party is a
wing, not a mode. I wouldn't have my CMDR wing with someone I knew would be hostile (except as a means of confronting them), but getting bent out of shape because another player had their CMDR be hostile to your CMDR is little different than being angry at the GM in a tabletop RPG when they get killed by an NPC, or angry at another player for what their character does in a competitive scenario.
As for bullying, there is no bullying tolerated between players in my tabletop RPGs, but everyone expects a fair portion of those characters with in-game power to use it to get their way, and most players are are just as willing to have their PCs use the implication or show of force for the same purpose. The PC's patron might blackmail the PCs, or one PC might resort to a threat of force to keep another in-line in a pinch. The overwhelming majority of the time this isn't representative of any player vs. player or player vs. GM animosity.
In the end, a player in Open in ED has no reasonable expectation for all other CMDRs to be friendly, for any confrontation with another CMDR to be fair (outside of the expectation that the player of that CMDR is adhering to the rules), or that one
character bullying another isn't entirely legitimate gameplay.