From what you're seeing does it seem to you like this is a pickup that could be wired series/single/parallel? I don't want to cut anything if not. If so, I don't mind cutting those wires in the middle and then extending them by soldering more wire to the ends.
It's definitely two coils in series.
C is the hot side of one of the coils. Let's call that one the First coil and the other one is the Second coil.
Between A and E, I believe one of them is the common on Second coil, and one of them is the pickup's internal shielding. They're tied together because that makes it convenient to have a single wire. You won't need to cut that blue wire for now. It's AOK as is.
The magic is B and D. One of them is First coil common, the other one is Second coil hot. Right now they're tied together by the red wire to put the pickup in series.
What we'll need to do to let you wire this pickup now is for you to determine which coil B is attached to and which coil D is attached to.
Leave the blue wire alone.
Cut the only the red wire, then measure ohms again:
B to C
B to A
D to C
D to A
With those results, we can know which terminal is attached to which coil, and then get you wired up with a four-conductor pickup that you can do series, single or parallel on!