Our washing machine has begun to smell like stank pond/septic tank
when it runs. I couldn't figure out why. I thought it could be
septic backing up, but there's a trap.

I popped off the cup on top of the agitator, the cup that you put
fabric softener in. Underneath was the most God awful, putrid,
disgusting black goop that I'd ever seen/smelled.

It was equivalent to cleaning out a shower drain.

I put it back on without cleaning it, figured I'll deal with it
tomorrow (sorry, Ben Franklin).

Can I soak the plastic cup and parts in an Oxy Clean solution? Is
that okay for plastic?