i was hoping someone else had more than a passing familiarity with this international order, and so knew why comparison to religion is warranted.
i would go further and argue that we can't fully understand US history and the history of religion in the West without going back to the late 17th / early 18th century and starting over.. this time *including* Freemasonry as an integral component in the larger story of Europeans on the world stage. *especially* America.. and not just North America.
simon bolivar was a freemason. so was prince piotr kropotkin.
so was the black abolitionist Prince Hall.. https://en.wikipedia.org/wiki/Prince_Hall
..after whom 'Prince Hall Freemasonry' was named.. https://en.wikipedia.org/wiki/Prince_Hall_Freemasonry
and you are spot on about 'Eastern Star'.. it is the 'ladies auxiliary' and was invented centuries after the fact to deflect from opening membership. 'Prince Hall' is a similar 'auxiliary order' for black men.
conspiracy theorists have all but ruined the topic for serious discussion, but that doesn't change what happened in history.