There are essentially three "factions" in the game: the Co-operative, the Offenders/Fugitives and the Thargoids. The Thargoids we can ignore for just now as they're not a faction which the player can join. However, the player can be either Clean, and therefore at least technically speaking a member of the Co-operative, or the player can have a criminal rating, which puts them among the Offenders.
At the moment, though, even if a player has a whopping great bounty on their head, they'll still be attacked by any pirate ships they run in to. There is no reason why this shouldn't happen sometimes: low types often fall to fighting among themselves.

If players were assigned a reputation, which for convenience I'll call "BAD REP", based on a combination of their level of bounty and their kill count, this could be used to calculate the chances of being attacked by pirates (and by bounty hunters and police, too). A Poor player with a bounty of, say, 15, would be more likely to be attacked by pirates than a Dangerous player with a bounty of 5. This could be modified by a variable based on the number of kills made in a particular system, with the variable being dropped substantially whenever the player makes a witchjump. The more kills made in one system, the higher the Bad Rep gets and the less chance of being attacked by pirates. Jump out, though, and your Bad Rep will quickly sink back to its "true" level. So if there was a pirate base in a system, a player with a decent criminal reputation could fly up to it and probably not get attacked by any of the pirates hanging about round there. If some pirates did attack, the player would only have to shoot a few of them – boosting the in-system kill variable, and boosting their Bad Rep in that system – before the rest got the message and left the player alone. Even a Clean player, if they've spent a lot of time slaughtering pirates in one system, might start to acquire enough of a Bad Rep for some pirates to think twice before attacking them.
If the game can treat players and NPCs as members of factions, then it might make things like friendly-fire incidents easier to cope with. This could be done by using the player's Bad Rep. A Clean player hitting a Clean NPC wouldn't immediately trigger a hostile response: it would just increase the player's Bad Rep by a point or two (or several – I haven't worked out what sizes these variables need to be) and maybe trigger some abuse on the comms. A hostile response wouldn't be triggered until the Bad Rep reached a critical threshold. This should happen fairly quickly, of course: it shouldn't take long for a merchant to realise that a Clean player is attacking them and hasn't just hit them by accident. But if should be OK for the player to scorch someone's paintwork, once, by accident, without everyone getting hot and heavy on them. Other factions, particularly the Thargoids, could be told to ignore incoming fire from members of the same faction, avoiding any green-on-green unpleasantness.
Thinking about it, one way to calculate the player's Bad Rep might be something like
(Bounty x Ranking + (in-system kills x10))/2
"Ranking" would be something like
<16 kills: 0 (i.e. Harmless and Mostly Harmless)
>15 and <32 kills: 1 (Poor and Average)
>31 and <128 kills: 2 (Above Average and Competent)
>127 and <6400 kills: 3 (Dangerous and Deadly)
>6400: 4 (Elite)
The result would be a % chance of pirate NPCs leaving you alone: so a Dangerous player, with a 40-cred bounty and no in-system kills, would have a 60% chance of being left alone. For every ship they killed in the system, it would increase their chances of being left alone by 5%.
I have no idea how easy or hard this might be to implement, or indeed what unintended complications might arise. Opinions (is this sort of behavioural change desirable, for instance?), refinements, scorn etc. would be welcome.