You aren’t providing the service across the border. The service is in your own country. The buyer is using telecommunications to make an order across the border.
The buyer is the one responsible for knowing their own local laws and should be responsible for managing them.
If a Saudi Arabian couple ordered a gay wedding cake from a baker in Montreal, over the phone from Saudi Arabia, in preparation for flying to Canada to get married, which laws apply? To whom?
Except the EU resident isn't "visiting" your business, you're providing a service to them across the US-EU border (and just like any cross-border service there are rules). I really don't get why this case is any more complicated than any other kind of consumer law (you can't sell electronics that blatantly catch fire to Australian customers, even if you're based in a country where consumer laws don't exist).