Socialism is the workers owning the means of production. There's a bit more than that, obviously, but it's in the end the one thing you need to believe in to be a socialist. You don't need to follow Marxist thought to the letter, you don't need to believe in the immediate destruction of all heirarchy, you don't even necessarily need to believe in the anti-racism and anti-nationalism aspects most embrace, but you do need to believe that.

A lot of socialist thinkers believe in mutual aid programs and such but just because a community or nation co-operates towards a mutually beneficial, presumably not-for-profit goal that doesn't make it a socialist program.

The army is not socialism. The mail service is not socialism. Police are not socialism. Food banks aren't even socialism, they're just a charitable organization.

Hell, unions aren't socialism in and of themselves, but you'll never catch a socialist criticizing the idea.

All of these are just fundamentally acceptable things for any kind of government to do, be it socialist, liberal, fascist, whatever, under any system except the most hare-brained versions of anarcho-capitalism.

America is just so fucked in the head by Randian neoliberal thought it just confuses any form of beneficial community action as socialism.

So, all that said, a group of churches putting together a mutually beneficial insurance group?

Not socialism. Especially given how many churches are investing their funds into for-profit businesses and property these days.

Now if the churches decided the best way to organize the insurance scheme was to create a worker co-op to run it you'd be on to something.