the railroad is closer to non-marxist anarchists more than anything, they only really stand for the abolition of certain things rather than the creation of new social institutions, like anything which could reasonable reconcile the usage of synths as sleeper agents by the institute with actually living in society.
The Institute is basically the epic bacon elon musk dictatorship except they can actually create stuff reliably, which makes them more terrifying because they will regularly undermine society more generally with their dumb ideas with nobody asking for it. they kill and replace people almost for giggles it feels like sometimes and they are so up their academic asses that they hardly realize they accidentally created wholly sapient machines. They don't want to build anything concrete as much as just lazily co-opt whatever other people build on the surface and inject their techno-bauble nonsense into it behind their backs, its how the first government in the commonwealth collapsed.
the BoS/Minutemen are actually fairly similar, the BoS are just far more structured. They are both essentially paramilitaries which promise self-rule and protection to settlements in exchange for access to their resources (the BoS very specifically for food and technology, the Minutemen more generally wanting some of everything), while also recruiting from these local populations and using the pooled resources they have to develop the wasteland into proper civilization again. The BoS are arguably better at it and more prosperous than the Minutemen because they completely cleared out the Capital Wasteland which was pretty hellish comparative to basically everywhere else in the setting, but if you want a more libertine and local polity the Minutemen are the better choice.
Mind this kind of local recruitment inherently does tend to drag along the various biases of the wastelands into the organizations though - be it anti-synth, anti-ghoul, anti-super mutant, ect. bigotry. The BoS out west is hilariously far more tolerant of mutants compared to the East Coast BoS because them being an insular debate club has basically figured out they aren't as imminent a threat to the continued survival of humanity anymore, while the East Coast BoS still burns with rage from the biases of their local recruits.