The brake system functions normally with or without the ABS being active. The only possibility that the ABS can interfere with the operation of the brakes is if there is a mechanical failure of the ABS unit. The regular brakes should function normally regardless of removing the fuse!
I think your problem may be that the rear brakes are doing the work and the fronts are not. This could possible be the master cylinder that has failed and depending on how the brakes where bled, the act of bleeding could have contributed. I think it would be worth going around and bleeding the wheel cylinders and calipers one more time just to make sure there is no air in the system.
Did you install any new brake parts?