Now, I'm sure they don't check. They probably don't pray, they won't quiz me about what church I go to. I could lie.
But I don't want to. I don't want to have to.
The exception is the Rotary Society. The average Rotarian is male, white, and 58 years old.
I was actively involved in Rotary in the 90s/00s via a Rotaract Club (for 18-30yos), and even then, there were many women, many non-white members, and plenty of people under 50 in the Rotary clubs I visited.
If some clubs/areas are still dominated by white, older males, it is mostly due to the difficulty in attracting any new members into volunteer organisations these days (mostly as it's unfashionable and people have other things to do), not due to any exclusionist policies.