Depending on your pressure setting, and the amount of pressure differential over your oil separator, yes this could be the cause.

The pressure is sensed / regulated at the exit of the air compressor. The safety valve is located on the separator vessel, before the separator filter.

Say you have your compressor set at 7 bar (100psi) and the delta-P (pressure differential) over your separator filter is 1.5 bar (22 psi)

This might not be enough to pop the safety valve, or it might be.

This means that the pressure before the oil separator is maximum 7 + 1.5 = 8.5 bar (122 psi).

This could also cause that the compressor never reaches the maximum set pressure and thus never unloads.

Of course the separator needs to be replaced as soon as possible, but there could be a problem with the inlet valve (loading/unloading valve) or the control system as well.

There's an easy check you can do (even with the dirty oil separator installed):

Slowly close the outlet valve until it is completely closed. What happens? Does the compressor unload? Does the safety pop again?

When the outlet valve is closed, there is no air-flow, just pressure. Air-flow creates pressure drop. So without air-flow there is no pressure-drop over the oil separator filter.

If your compressor now reaches it's setpoint and unloads, than the problem is your separator filter.

If it still doesn't unload but keeps loading and pops the safety instead.. then the problem is with the control system / inlet valve.

Not clear from your question, but does it not unload all the time (every time)? Or does the safety valve just pops throughout the day?

Since the pressure differential is depended on air flow, this safety-valve-popping probably only occurs at times of high compressed air use. At that time, the air flow is high, so the pressure differential is high. At times of lower air consumption, the pressure differential will be smaller (that's why we closed the outlet valve for testing purposes).

One last thing: if the safety valve has popped a few times, it can become 'weak' and pop at a lower pressure than originally. So you will have to check your pressure gauge to see at what pressure the valve pops.

Hope this helps! Good luck and wold love to hear how it works after you changed the oil separator of when you did the check i explained.

good luck!