This has been one of the advantages of petroleum: the ability to make the same or similar product without concerns like this. Latex, for example.

It looks like this specific process has a lot more going on compared to latex but your question is valid and would need to be addressed.

It's very unlikely that you would experience any problems. Drug synthesis such as this involves multiple reaction steps, precipitations, washes, and filtrations to produce the final purified active compound. If they're creating acetaminophen, that final product is going to be pretty much pure acetaminophen with only trace amounts of impurities. Not enough to cause issues.