I'm not worried about this, Ron. There's nothing basically wrong with showing up at other churches, be they Christian or anything else.
To me, what matters is our identity. We (the little-c catholic church) are all supposed to identify with Christ, and with each other. About 50 or so of us also identify with a little body known as The Village.
My point is, you can go anywhere and do (almost) anything and still have that identity. So if Cori goes someplace else for her class, she can worship Christ there. If she wants, she can come back and tell us about what it was like - which integrates the experience with the larger community.
God is still there, happy to be worshipped, even when the people in a place don't have great theology. That's good, because otherwise we'd *all* be in trouble.