Sorry, but I must contest the assessment of present-day situation on which you base your question. Do have any examples that make you believe that the US of the year 1997 was significantly more religious than „Europe“?

E.g. Germany had then been ruled by the CDU for about 15 years. CDU stands for „Christlich Demokratische Union“/“Christian Democratic Union“, which does not really fit into „marginalized religion“. If I was more into GDR history, I could write about religious organizations that helped to bring about the „Wende“, e.g. with persons such as Joachim Gauck. I could also write with Church taxes, publicly funded Church-run schools, religious education in public schools, the fact that the vast majority of public holidays in Germany have religious names, that shops are closed on Sunday ,... all of which run counter to the notion of „secular“ Europe, but that's outside the immediate realm of politics, the topic you asked about.

The concept of Europe as a more secular place than the US is first and foremost an opinion and one closely tied to modern politics at that. A more open-minded question could acknowledge this.You should also drop the „still“ from the question, as it assumes a certain view on how history and civilization should develop, sometimes called „Whig history“. Therefore, I would encourage you to resubmit your question as „How did the perception that religion is more embedded in the US than in Europe develop?“.

Or you could ask about a specific country that actually puts strong emphasis on laicite, such as France, and about the specific context under which that public consensus evolved, because, quite frankly, the question as it is is very broad and there is no one-size-fits-all for all of Europe. To give you a rough outline of how diverse the relationships of European states and religion are, consider that France's approach to secularism was shaped by specific decisions taken during the Revolution (if you are an avid reader, you could read Doyle's „The Oxford History of the French Revolution“) and subsequent events. Germany's approach is shaped by a cocktail of interactions of Catholicism and Protestantism, nationalism and of course the events of the 20th century. Spain's approach was shaped by the Civil War, an event which is completely absent in, say, Swedish history. Poland's approach was shaped by being part of the Warsaw Pact and the Polish Catholic Church's reaction to socialist rule. Italy had an issue with the Church State, which shaped the Italian Republic's interaction with Catholicism. And this is not even scratching the surface.