Yea, having grown up in a heavily churched background and having attended churches in WV, KY, TN, AL, FL growing up, I would agree. In the non-denominational churches and in less formal denominations (Church of God, Nazarene and to some extent, Baptist), I always felt welcome dropping into a random church service, meeting the people, etc. Everyone was always welcoming and had a strong sense of community. There were very strong personal bonds. When you get into the smaller, poorer communities, the bonds cross over into VERY personal territory... where the members often understood the financial & family troubles of each others... that takes a lot of trust to build that. To some extent, that was their support network and that's how they made it week to week. In all those, I was always welcome as a stranger. Very good people.
I can say that when I attended a Unitarian church here in Rochester, MN, it felt as welcoming as any other church here in town. I don't know if you would count that as "non-religious" or not, but they are definitely not dogma- or doctrine-motivated. It was larger and more formal, but the formality was a function of its size, not the spirit of the people.