Dude, ping me with your lodge number and I will definitely visit if I'm in your city.
Part of what attracted me to Freemasonry was the quality of their enemies, as whatever those accusers had a problem with, I was pretty sure I wanted to be on the other team. The other thing was finding the pigpen cipher doing security work. It's so not-secret I don't mind being relatively open about it, as you know that every other guy you meet in it had to be vetted as not a total danger to himself and others.
The other part that interested me was a (perhaps apocryphal) story about how lodges in the UK were instrumental as neutral territory between religious partisans during the Troubles, and other stories about the idea of a persistent commitment to meeting on the level with men as peers that transcends the official politics of the day. To me, this is a crucial part of the fabric of civil society, just as much as the Chatham House rule is. We need this ability to have honest discussions as individuals now more than ever. There's a rule you don't use the privacy of lodge to discuss politics or religion, but outside, guys who would be on the opposite sides of a civil war right now sit and listen to each other over pints, test ideas, and really listen on the basis that dozens of other guys say this guy is ok, so even if I don't agree with him, there's something valuable about his experience. The continuity of basic fraternity among men as an essential principle of civic life is what religions and politics fundamentally lack.
I think the high bar is the theism, as that's probably the only irreconcilable difference in beliefs, as the logic of ideas from the axioms of theism vs. atheism are just alien to one another.
Men being able to meet and relate as equals outside their public lives requires a level of trust that only comes with the mutual guarantees of privacy. It sounds meta, but really, imagine just having a lot of friends you trusted and who would give you the benefit of the doubt, but had enough distance like co-workers where you weren't very judgmental of each other.
The secrecy aspect is really about setting a personal boundary, where the few secrets themselves are yours to keep, and this ability to have something that is yours, whereby there is a you independent of your other relationships, and that is a foundation for breaking co-dependency habits and other boyhood things a lot of guys never manage to grow past.
It's a very mixed bag, but you see where you are, and where other guys are at different stages of their lives and circumstances. It does seem unlikely in hindsight that a committed Catholic partisan would defy the papal bull, risking excommunication, and accept initiation into masonry, but the principles of masonry, encoded in allegories and a kind of memory palace (the method of loci) of symbols gives you a set of reference ideals you can measure your own character by and develop personally against them.
Lumping masonry in with secret socieities and cults is pretty dumb. When I hear conspiracy theories about masons, I always ask, "cui bono?" Who benefits from discouraging good men looking for moral and ethical lessons from finding each other and recognizing each other as equals? When you look at historical movements against fraternal organizations, it's worth asking, who fears good men?
Anyway, looking back, all it has cost me is the ability to give short answers.