I'm not talking about multinationals doing business at both sides of the ocean* nor individuals. I'm talking about diplomacy and governance. The potential American envoy to the EU is openly hostile towards the EU and wishes to break it down. This is a fact. An unprecedented one. The WH's chief strategist also has the same aims.
America and the EU won't become warring actors, but they won't remain in friendly terms. Barring some surprising events, there's going to be mutual distrust from now on. At best, our relationship is going to go from close and friendly to neutral and seeded with wariness.
*this may also change depending on economic policies.
Doesn't a US retrenchment implicitly weaken the hold of EU institutions though in the long run?
Right now, the US essentially subsidizes European defense costs against other international actors like Russia and arguably China if they continue to saber rattle and begin to exert economic pressure against the EU.
The new paradigm of realpolitik is going to require Europe to step up its acquisition of military hard power in order to be taken seriously. Those funds are going to have be shifted either from national budgets to an EU army--which poses its own set of difficult questions to EU members-- or from social program budgets which IMO will exacerbate the populist question in Europe.