You probably already know this, but just to be on the safe side: Avoid acidic cleaning agents like bleach.
Also be careful to avoid situations that might expose the webbing to battery acid. It's very bad for nylon.
As others suggested, I wash my climbing ropes and other nylon soft gear with woolite. Were I to need to wash my seat belt webbing, that's how I'd do it.
https://www.cmcpro.com/what-happens-...ts-on-my-rope/
--Bob K.