Which aspect of this do you disagree with? That the US has become less religious? More secular? Or that despite our secularism we often remain dogmatic about our political beliefs and their centrality to our lives in ways that mirror religion?
As I said in my edit, it's too simplistic and vague of a framework to adress this in depth. I believe our relationship to religion has changed, but I don't think we can say that society, as a whole, has become more or less secular as a result of it. I also think that talking about "past centuries" in this manner makes it even less useful, because our relationship with religion has, again, changed significantly at several points in the past three centuries to an extent that would probably fill volumes of discussion, and here is especially notable a pretty stark distinction between Europe and the US, urban and rural spaces, intellectuals and uneducated masses etc. that I feel is often swept under the table in favor of broad overly general statements.
The one thing I feel could be adressed in this small space is the change in the politization of religion from 1970 to now, where again we have a fairly stark divide between American politics, British politics, and continental European politics (and even here, Western/Central and Eastern Europe provide stark contrasts). In brief, while there have been great advances in the secularization of legal frameworks in the US (Roe vs. Wade, legalization of gay marriage) we have also seen a re-emergence of political religion to an extent that had been dormant since the prohibition era, if not earlier. I am of course, referring to the great alliance of corporate-conservativism on one hand, and the religious right on the other, but there had been moral panics that had already shown the increased interconnectedness of conservative politics, suburban culture, and religiously motivated moralist zealotry.
In Europe, we see a different development, where the secularization comes later but much more starkly with the waves of marriage equality of the early 2000s, but similarly a much stronger return of political religion as an instrument of right-wing political mobilization. Here, we have in particular the politicization of religion as a marker of ethnicity, with "Judeo-Christian" Europeans on one hand and "Islamic" non-Europeans on the other (the "Judeo" part of this otherwise very Christian construction is important, as it allows for a political alliance between the otherwise antisemitically-inclined European nationalist right with Israel and its own ethno-religious pillar serving nationalist-conservative policies). From there, we see a rapid conflation of European conservative-nationalism with Christian religion on one hand, and the reduction of non-European ethnicities to a singular "Islamic" entity, propelling us into our current mess.
As you can see plainly, my view on this issue is a rather complicated, tangled mess that doesn't really fit very well into the framework you previously laid out.