I did some searching, admittedly not extensively, and I'm sure this question has come up before but alas, I'm just going to ask again.
Let's say I'm Bounty Hunting in my PMF's home system and I come across a wanted ship that's owned by an NPC belonging to my PMF. Under what conditions, if any, should I kill it? What would be the net effect on my PMF?
Tl;dr nothing, go for it.
The faction a ship belongs to its, for the most part, irrelevant, for the purposes of general combat[1]. BGS effects are achieved through two events in combat.
- positive security and influence effects are obtained for the faction who issued the bounty, in the system you hand the voucher in
- negative security effects are obtained for the jurisdiction of a faction where a crime is committed.
Note neither of these care for the ships allegience... only for the jurisdiction who issues a reward or who a crime is incurred.
in this specific case, you kill the wanted ship owned by faction A, faction A gives you a bounty reward, cash it in system A, faction A gets benefit.
[1] that is, I've come across a random ship in space, what happens if i kill it, without consideration to CZs, local jurisdictions and such.