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This thread could use a comment from the LCMS perspective.
In the LCMS, we practice (or are supposed to practice) "Closed Communion," that is, we commune only members of churches with which we are in fellowship. The church to which a person belongs is their public confession of the faith. Thus, since the Church of Rome and the Lutheran Church-Missouri Synod are not in fellowship, I would not commune a Roman Catholic, nor would I expect to be communed at a Roman Catholic church.
Closed Communion is not something unique to the LCMS. It is the historic Christian practice. It has its roots in the early church, when, if you were wanting to commune at a church in another country, for example, you would need to bring a letter from your bishop, attesting to your orthodoxy.