If you believe in the Church, you should prefer everyone adhere to God's commands, which you can believe while still opening your arms to those who don't.

I think we can both agree that BYU represents the church to some degree and I prefer when people wearing that representation reflect the ideals of the sponsoring institution. I'm not bothered when people don't, but I prefer when they do.

To answer your questions more directly 1 I care because I am also associated with BYU and the sponsoring institution and believe in its message. And 2 people should always come to church regardless of the circumstances, I'm not sure the tie-in you are trying to make there.