They’re a kind of Conservative Jews.

Ben, you’re mistaken.
Reconstructionist Judaism (?) has an atheistic or deistic outlook that sees cultural value in various traditional customs.

They split off from the Conservatives. See Wikipedia.

I’d suggest not discussing this based on labels (Conservative or not), but based on the substance.
I read a bit on Wikipedia, and at first glance it seems to me like complete nonsense. A kind of folksiness of some sort, just not on a national basis but on something more universal. But as I said, that was a one-minute read (which really didn’t make me want to look into it any further).