You have to keep in mind why people join secret societies. Generally, it's to escape society's norms. Therefore, you can extrapolate that when the US was more religious, such organizations would not be. Furthermore, you can conclude that many of these organizations will be different in different cultures. There will be differences and even cultural divisions amongst these groups, so just because a society is religious one organization could be angry that they're deists while another could feel like society isn't religious enough. Whatever their beliefs are, they often don't feel comfortable enough to air them publicly which can be due to social ostracization or thanks to political officers/police. Way back when it was difficult to discuss anything without fear of creating mass hysteria or risking the king dropping a permaban hammer on your head. So at one point in time, some of these organizations probably were the modern-day equivalent of professors sharing peer-reviewed studies. Ironically if the culture in the US continues to shift to the left and people can't express their feelings regarding the left's sacred cows, these types of organizations will likely draw and attract more conservatives. Or perhaps these type of people will create their own organizations.
I am not a mason or in any such group, but I have run into a couple of them in the US and even in LATAM. In both instances, they were men older than me and it seemed to me to be a geriatric organization for lonely middle-aged and elderly men who wanted to feel special/empowered. In Latin America, they came across more like a religion. They were not very fond of Catholicism and were more left-wing than the rest of the populace. In the US at least to me, they seem more like old guys trying to network because they're elderly, bored, and want to hawk goods. It was a small sample size but they reminded me of some of the boomers that spam posts about 1776 and 'don't tread on me.'