You are correct that the law is still there, but it's the difference between innocent until proven guilty and guilty until proven innocent.
One is just accepting payments, the other is processing them for vast amounts of third parties.
Because money laundering can happen at any level, and specific regulations apply, you don't need to be a card payment processor processing "payments for vast amounts of third parties".
As long as you accept payments, even for a lemonade stand in the corner, you need to comply with these.
In fact you probably misunderstood what Stripe demanded on the parent's situation: they didn't demanded the parent's store comply with the same regulations Stripe does as a card payment processor. They demanded they comply with the regulations a store should comply with.
If your cryptocurrency-based store wouldn't comply by the same regulations that third party was required to comply with, though, then you, as a merchant, would be breaking the law. Which takes you back to square one, cryptocurrency or not.
It's just that with cryptocurrency you get to decide to break the law and continue accepting payments, instead of being based to Stripe.