Fellowship

Come to think of it, I have a second question. In the spirit of unity, do we as Christians fellowship everyone who has been baptized, regardless of their other beliefs? Was the man in I Corinthians 5:1 still in fellowship with the rest of the church? If so, why did Paul say they should have rather mourned his actions? I guess the question is, if a person or a group has been baptized for the remission of their sins, is that absolutely the only test of fellowship?