Reasons for fellowship practice
Recently I went to a funeral for a family member who, to my knowledge, did not attend church. The service was led by a pastor from hospice and I believe he was non-denominational. A WELS pastor who sat next to me refrained from singing and praying the Lord's Prayer. The hymns were out of our hymnal with no chance of being improper. Why do we refrain from praying and singing with other religions?
A paragraph from This We Believe answers your question succinctly: “6. We believe that those whose confession of faith reveals that they are united in the doctrines of Scripture will express their fellowship in Christ as occasion permits (Ephesians 4:3). They may express their fellowship by joint worship, by joint proclamation of the gospel, by joining in Holy Communion, by joint prayer, and by joint church work. God directs believers not to practice religious fellowship with those whose confession and actions reveal that they teach, tolerate, support, or defend error (2 John 10,11). When error appears in the church, Christians will try to preserve their fellowship by patiently admonishing the offenders, in the hope that they will turn from their error (2 Timothy 2:25,26; Titus 3:10). But the Lord commands believers not to practice church fellowship with people who persist in teaching or adhering to beliefs that are false (Romans 16:17,18).”