Water continues to fill the tub even when the machine is off! Our water supply valve is the only way to make it stop filling!

Question edited for clarity. 'field cycle' to fill cycle.

Do you hear water running? Water inlet valve failed.

or

Taking too long to fill. Check the strainers in the rear where the hose connects and check water flow from the hose.

Also try a power disconnect overnight to do a power reset of the control board.

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If the cold water supply is slow or not entering the tub at all, the washer will stop ahead of the rinse cycle while waiting for the tub to fill. This can be caused by a clogged water inlet valve, the main water supply valve being partially closed, or low water supply pressure from the home.

Crosley Washer stops mid cycle - Repair Clinic

https://www.google.com/search?q=Crosley+Professional+Washer+washer+stopping+at+beginning+of+fill+cycle

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That sounds like the cold water valve has failed. Replace it and you will fix your problem. Those valves were not designed to be repaired.

Close the water supply valve and allow the machine to completely drain the water from the tub. Turn off the machine and disconnect it from the power outlet. Open the water supply valve. Replace the water inlet valve if water drips into the tub when the machine is off.

Start a new cycle if the machine stops filling when it is off. The control board or the water level switch is malfunctioning if it keeps filling even during the spin cycle. Indicate the model number for proper troubleshooting and repair assistance.

This sounds like your water fill valve is bad and will need to be replaced.

If water is overflowing and you disconnect power to the machine. then:
A. It continues to fill: Replace water fill valve. (the part the fill hoses screw onto)
B. It stops filling: Most likely has a plugged tube from the tub to the water level switch.

if you can turn the washer off while it is still filling. and the water continues to enter the machine you have a bad inlet valve.
Do me a favor turn the washer to fill, with the washer still running unplug from the wall. If the water is still entering the unit you have a bad inlet valve

try turning the mach off while it is spinning and filling.if it continues to fill or drip heavy,the mixing valve is not closing completely and needs to be replaced.if the water stops when the mach is turned off,there is a problem with the pressure switch.

The cold water valve is probably stuck open. It should open only when there is voltage across the valve. It could just be clogged inside. If you can remove it, you might be be able to take it apart and clean it. Just make a note of how parts fit together as you are taking it apart. Clean all parts with old toothbrush and reassamble. Before you reinstall, connect it to a garden hose outside. No water should come out when you turn the hose on. If it still fails, just buy a new valve.

A defective pressure switch can interfere with the cycles that depend upon the switch to indicate when water has filled or emptied from the tub. It can also result in underfilling or overfilling of the tub. The switch routes current from the timer control to the temperature switch and the water inlet valve when the tub needs to be filled. Once full, the pressure switch cuts the current and reroutes it to the motor on the timer control to continue the cycle.

Does it stop filling when you hit Start/pause or do you have to shut off water supply? The air dome is the black rubber piece that is clamped to the pump housing. Usually i find that clogged not letting the pressure sw operate proper. I belive the switch has 4 wires. It has 2 contacts, one closes with a small amount of water visible in tub, hi contacts close with water much higher - even filling bottom of boot.