This question was posed recently in a group I'm a part of, and I thought it was worth answering from my perspective because I'm a former Protestant who only very gradually became Catholic in his thinking.
One thing to note is that this is an issue that is not specific to Catholics. Members of Eastern Orthodox or Coptic Orthodox congregations who grew up primarily in the U.S. often have the same struggle of trying to reconcile their deeply-ingrained and culturally-acquired assumptions that stem from Protestant thinking with the ancient Christian religious tradition which predates such thinking and is different from it at a paradigmatic level.
This is not even an issue that is specific to members of Christian groups. Jews, Muslims, Buddhists, people who are part of various Indian traditions under the umbrella of Hinduism, and so on are often afflicted with this difficulty as well. That said, I'm going to examine the situation of Christianity in particular.
We who were raised in America generally inherit a set of intuitions about the meaning of the word "worship" and the word "pray", the nature of human social hierarchies, the nature of our relationship with religion, the place of the Bible in Christian life, the nature of the Church, what it means to be a Christian, and so on.
Because the United States was heavily influenced by Protestant Christians in its culture, its theological language, its popular ecclesiology, its view of the Bible, and its view of human nature, these intuitions are often Protestant intuitions.
I wrote a fairly lengthy series about my own journey to re-examining and ultimately rejecting those intuitions, and that was not an easy process, given how basic many of them are to someone raised in the United States.
For example, it took me quite a long time to shake the intuition that the Bible is the basis for Christian theological claims and truly understand that the Bible is a written record of early Christian theological claims. I thought that the Bible was what gave Christianity the authority. It turns out that Christian authority vested in the Church gave us the Bible.
It also took me many years to understand why my intuition that Mary's role as Queen of Heaven need not be emphasized was wrong, and to unpack the ways in which my American understanding of social hierarchy had unfairly prejudiced my view of the divine hierarchy.
I also had a defective understanding of my relationship to the Church. I viewed the Church as something I could accept or reject on intellectual grounds, not as the Body of Christ in its earthly fullness to be loved as I love my own body, just as Christ loves the Church.
This intuition that turned out to be false isn't something I developed on my own. I inherited it from an American culture that has largely agreed that attending churches is just a matter of individual preference in practice, even if in theory some of the congregations assent to the traditional ecclesiological view of the 1st-millennium Church that there is one true Church, and outside the one true Church of Christ there is no salvation.
In a similar way, there are many people in the United States who are raised Catholic and nonetheless take the typical post-Reformation view that leaving the Catholic Church to attend services with another congregation is just their personal choice. It's not a schism or anything serious like that. It's just a matter of doing what their conscience tells them.
And given this, it's not surprising that Americans don't see the Catholic Church as an authority to be obeyed, but rather an advisor on morality whose advice can be ignored, because the individual is the final arbiter of what is best for the individual. The Church can't really be an authority over an individual, because the individual is the ultimate authority.
This American individualism is so deeply rooted in the psyche of most Americans that even the most traditional Catholics who strive for obedience to the Church can struggle with it, sometimes going so far as to set themselves against the Church for not living up to their individual standards.
While some might focus on the problem with Protestant theological language flattening the definitions of the words "pray" and "worship" (for good reasons), I am more concerned about the more deeply-rooted intuitions which make it easy for us to rationalize leaving the Church or rejecting Her teaching while still being attached to the Church for other reasons.
Intuitions like these are doing real damage to the Corpus Christi, as they motivate an increasing number to leave, many to dissent, and some to grumble against the Church for not doing more to strike against those who dissent.
Though it's interesting to consider how American culture tends to make even Catholics and members of other ancient religious groups accept intuitions at odds with how their religious traditions understand the world, it's mostly just sad to watch the Body of Christ breaking again.
Ut unum sint.
Related: The Protestant Intuition: Divine Gifts & Human Works
Note: Above is a picture of Martin Luther's edited Bible translated into German.