I’m significantly allergic to pine. I wonder if this means I would no longer be able to take these medications if industry switched to this method.

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.