I think you make some great points, Ritter.
If someone tells me "I go to SOUTHSIDE CHRISTIAN CHURCH OF JESUS CHRIST WHO WAS IS AND FOREVER WILL BE AND DIED FOR OUR SINS SO WE COULD HAVE ETERNAL LIFE MINISTRIES. It's conveniently located across from Wal-Mart." it doesn't mean much until I see if that specific person truly believes in the way that most others in said church or denomination do.
That's just true in general for me though. If someone says "I'm a Christian", it doesn't mean much to me until I can see what their walk is like and discuss things with them to see what is really there.
I also don't think I could consider someone who holds their specific church or denomination on such a high level that they believe everything spoken at the place and will agree with anything there even without praying, studying God's word, and testing it for themselves. I won't ever put a label on myself.
To the original poster: Yes, it can matter to me. There are some that do things I don't agree with, and hold to different beliefs, etc. My belief on salvation is the core thing, but some other things do matter.
Also, you mentioned Mormons. That's a whole other thing. I don't know how much you've looked into their belief system, but it wouldn't take too much looking to see just how different it is.