Which was only possible because of the lofty ideals.

Your original characterization: "America was built and designed to be a country that primarily existed for the landed white male gentry. Even other men couldn't vote for the first 100 years, and the whole system was a very carefully calculated pyramid of power and privilege. Not surprising, since that was pretty much all that our dear founders saw all around them as examples. Just as "religious liberty" was shorthand for "our brand of religious intolerance - just not the one we left behind""

The first part (non-italicized) part is largely true. But as the Smithsonian article that you quoted explains, the contemporary brand of religious intolerance was considered and rejected, and the relevant founders were very proud of the accomplishment. It was not shorthand for "our brand of religious intolerance". You cannot embrace religious freedom and simultaneously embrace substantial religious intolerance--once you embrace freedom you have nothing left to do with your intolerance besides say how put-out you are by other people following their sincere beliefs. The freedom constrains the intolerance immensely.

Religious intolerance by all rights, given that many of the settlers were practically religious extremists, should have been immense and often was, as you have cited. But pushback is and has been possible in the United States in large part because of the lofty ideals (and concomitant laws) which are widely lauded even while many people are blatantly failing to live up to them. It matters enormously--the Supreme Court wouldn't have had anything base a decision on in 1962 otherwise, for example.

Tossing that all on the same "oh, they just wanted religious intolerance" side is just completely wrong. It renders very natural and explicable trends incomprehensible, and also casts shade on one of the greatest weapons we have to fight religious intolerance right now.