You make good points, but let me insert a critical distinction into the conversation, namely the difference between church-going Evangelicals and Catholics in the United States.
The Evangelical movement has become a powerful political force in the US largely because Evangelical Americans solidly back conservative principles and reactionary lawmaking.
While the situation in the Catholic pews is complicated, it's not unfair to say almost the opposite is true there.
Catholic clergy tend to be highly conservative, even reactionary, on social issues like abortion and LGBTQ equality (probably because they have to hold conservative ideas on those matters to become members of the clergy), but the same cannot be said for ordinary Catholics.
In fact, on LGBTQ matters, Catholic lay people are slightly more likely than the general American public to be supportive of equality, and that means very supportive indeed. In this respect, ordinary Catholics hold diametrically opposed views to most (but not all) Catholic clergy. And even with the recent LGBTQ backlash, we're not seeing much change with that. Catholic lay people are becoming more liberal on LGBTQ matter, not less liberal.
Nancy Pelosi, who calls herself a devout Catholic and who recently traveled to Rome to meet with Pope Francis and receive communion from him, is a good example of Catholic lay people supporting reproductive freedom. Abortion is intensely controversial among Catholic clergy in the United States, but lay people generally don't vote or hold political views in accordance with what priests and bishops want.
The Democratic president of the United States, two liberal members of the Supreme Court, and the liberal Speaker of the House are Catholic, which might tend to uphold the idea that the United States is becoming a Catholic nation. But ... what does that really mean?
We can presume with a certain amount of accuracy that Evangelical political leaders and judges will hold intensely conservative political views. We can't presume that about Catholics in the United States. Indeed, the opposite is likely to be true.
(The Supreme Court is complicated, because justices vetted by the Federalist Society, a virtual requirement for Republican nomination, will always hold intensely conservative political views, whether they are Catholic or not.)
Catholics in the United States are diverse. They don't tend to share political points of view like Evangelical Christians do, and when they do they're more likely to be liberal than conservative.
Also, it should be pointed out that unlike with Evangelical Christians, a Catholic identity can say more about ethnic/family heritage than actual religious beliefs or practices.
Somebody who identifies as Baptist, for example, probably holds religious beliefs similar to most other Baptists. People don't say they're Baptist because it's their heritage, they say it because it's what they believe.
Catholics are different. Lots of people who identify as Catholics don't hold orthodox Catholic beliefs. But for many different reasons, "Catholic" is still an important part of their identity, wrapped up in their heritage.
So when we ask if the United States is becoming a Catholic nation, we need to be sure we're on the same page with what we're talking about.
Because people who identify as Catholic aren't necessarily in favor of values and politics we think about when we think about Catholicism.
