Might help to understand how the solenoid works.
Two big posts will pass current between them when the unit is activated.
The two small wires, regardless of color, attach to a coil of wire inside, arranged in the form of and electromagnet. When power is placed on those small wires, the magnet is energize and big shorting bar moves into position between those two big posts.
Solenoids with the black wire expect to be powered with + 12v on that wire, and ground, or more correctly Battery NEG, on the other to energize.
The little coil in the solenoid doesn't care how the circuit loop from/to battery is completed to energize. The circuit interrupter can be in the POS path or NEG path, to allow the solenoid to activate/deactivate.
Anyway, the wire colors match the year and model of the bike, but the solenoid still functions when power is applied across the small wires whatever their colors.
I don't see how this could effect you charging issues. Just how much of the bike wiring has been customized/altered?