Oz... seriously mate, how many Civics/CRXs to '90 had ABS????
Try none in the States, none in the rest of the world except for the SiR CRX/Civic - even then it was a much unused option.
Engage brain before opening mouth
To answer the question, it's warped rotors. They can be machined, but with the age of the car, machining them won't be a permanent solution as they will just go out of true again. Replace them. I'm doing the same with cross-drilled and slotted DBA rotors. The drums will be fine.
It's not your balance or alignment as you explain it as only happening under brakes.
One other check is to make sure the calipers are tightly bolted on. I doubt that they are loose, but it doesn't hurt to check