I've got an awful polypropylene stink within the cabinet of my bathroom sink.
Not having any trouble with the function of the sink, toilet or shower or plumbing under the sink.

It seems to get stronger when the shower is used.
What should I do?

What are your hot water supply pipes made of? What is your shower made of?

Polypropylene is used in thinner plastics, not water pipes. Do you mean PEX (polyethylene) or PVC (poly vinyl chloride) used in plumbing, the most common?
Polybutylene was a flexible line used until the 90s when it was shown to wear out much too fast.
I suppose a hot water pipe could smell, even if a copper on is right against something plastic.