I think you won't get kicked out of the faction unless you kill a named character or too many unnamed (not sure about the second).
Kill any nameless paladin you wants. It won't affect the game in any way.
You can pickpocket them as well. Go into sneak and you can see the item they carry.
Shoot their fusion core from stealth. It'll pop them and you'll be fine
They will agro when you attack, but it is not a permanent thing. Just kill them, loot their crap, then wait a few days before going back to the BoS, they should be friendly again. I snipe them from far away, it seems to stop all the others getting angry with you. You can normally snipe a few of them before anyone cops on what is happening.
The BoS wouldn't aggro even if you kill the randomly spawn BoS members. Only if you're at the base. I killed all the BoS members because Danse was with me, and they're totally ok with me after leaving Danse behind and teleport to the airship.
I didn't mean as a faction, but if there are a a few of them on a patrol, and you start shooting them, they will shoot back after a while. And if you kill a few of them, the rest of them become hostile, but only temporarily.
I believe one workaround is to have Danse with you, they would be hostile to you and you are allowed to shoot them, but if you let go of Danse then they will go back to normal without aggro.