It is pretty simple for me: either I know the person or someone in the group knows the person, and vouches for them. No further vetting is necessary. If the person comes and is a bad fit, further steps can be taken, but to get in the door, just being someone known by somebody in the group is enough.
Now in the case of recruiting someone unknown to flesh out the ranks, probably a few emails and a phone call are fine, just to get a sense of the person. I might say something like, "it doesn't matter what your political or religious affiliation are, but just so you know we like to have a few beers and make some off-color and occasionally non-pc jokes, but racism, homophobia, bigotry etc are not cool."
To be frank, I'd be very leery of joining a group that asked me to take a background check. I understand the reasoning of the OP, but it does set a tone of mistrust and is rather unfriendly. Further, emphasizing some kind of "probationary period"...that doesn't have to be spoken, but is generally understood that it has to be a good fit. I wouldn't want people to feel like they're on trial, even if the reality is that the first few sessions are an unspoken audition.