The liberty we enjoy derives from English legal and political tradition, in particular the Anglo-Scottish Enlightenment. Moreover, the enlightenment political traditions in both GB and the continent were aggressively opposed to clericalism and “established” churches of all kinds. Had this country been founded by the French or the Spanish, it would have been a very different place politically.
These strains of thought are rooted in a continuum of Catholic thinking and legal tradition, not merely ‘in spite of.’
Much of the liberty we enjoy derives from removing religion altogether from public life; while nominally “Christian”, there is no indication Christianity drove “Manifest Destiny” or the Monroe Doctrine.
It would have been different if France or Spain founded it, until today when we are in much the same place politically as both of them (socialist policies coupled with negative birthrates, with religion completely removed from the public sphere).