This was very easy to do, once upon a time! This was commonly called a “Lofty” after the pod pilot who made it so famous. Back in 2006, if not earlier, when you joined a gang you’d get a popup warning you that doing so would make you a war target if any current or future member of the gang was involved in a Corporation war. However even back in 2006, you couldn’t simply shoot a gang member just because they were in a gang with you. You had to manipulate the games mechanics first!
This is where the Lofty came in. For example, someone would ask for help in local with a mission. Some deluded naive chap would agree to help and join the gang (I don’t think they were Fleets back then!). The chap would then warp to the “mission”, but was in fact typically warping to a safe spot; just before the pilot would drop out of warp, two more pilots would then be invited to the gang…
However these two pilots would be in different Corporations (for example Corp A and Corp B) at war with each other.
So, in this scenario, Player 3 from Corporation A is at war with Player 4 from Corporation B. This was the kicker, as inviting player 3 from Corporation A into the gang would make everyone in the gang a valid war target for player 4 in Corporation B. However, you’d then invite player 4 from Corporation B into the gang and at that point EVERYONE is a valid war target for everyone else in the gang. The player dropping out of warp would have no chance to drop the gang before the first shot was landed, at which point the pretty faction fit mission ship was spit roasted by the one+ PVP fit boats. As a safeguard, they tended to have someone scanning ships to check fits as players undocked.
Another gripe was that the default action in response to a gang invite was the “accept” button. I nearly got caught by this as the gang invite grabs the window focus even if you are typing in a chat window. So if you don't touch type and hit return, you actually accept to join the gang :P Nasty…
People whined and spat their dummies out, and as ever CCP caved in and removed the “at war” risk of joining a gang. Now you have to put up with neutral fleet boosters etc. It was a shame as the warning was there for all to see. In reality it was the warning and invite mechanics that needed attention, not the gang membership mechanics.
So, this was how people were able to shoot gang members; as stated above, this still involved the manipulation of kill rights and didn’t happen just because you joined a gang. You had a clear warning and the option of clicking no. It is still possible now, but it’s just a lot harder and you have to rely entirely on player stupidity or ignorance rather than lack of reactions.
To answer the question directly! No it is not possible for gang members in different Corps to PVP with each other in Empire without Concorde intervention unless one of them obtains kill rights.