I don't think changing tyres affects the ABS.
Generally speaking the ABS compares the rotation speed of the front and rear wheel.
Let's say you brake very hard on the rear brake (locking the rear wheel) and leave the front untouched. The speed of the rear will reach 0 km\h if you lock the wheel , while the front is still spinning. Even before locking , the speed will be different .
The Anti-lock Braking System will detect the different speeds and release the rear brake pressure so the wheel spins again , avoiding locking and skidding. All that happens many many times per second.
Having bigger or smaller tyres does not change the concept of ABS.
I have wider rear tyres and if any , I feel more grip (than the OEM tyres)