It is possible for there to be a situation where to offer some service, you have to either break the laws of one country or the other. In this situation, you simply cannot offer that service without exposing yourself to legal consequences.
That's not always sufficient. You can end up in a situation where an American court demands records that concern European customers. In that situation, handing them over gets you penalized in an European court, and not handing them over gets you penalized in an American court. Both will have the ability to really hurt you, and "the other court tells me not to" is not a defense at either of them.