What is the best approach to talk to bothers or sisters in Christ who have decided to worship at a denomination? One of the main comments I get from these brothers and sisters is “the church they now worship at teaches the same thing as the church does only it doesn’t say the Church of Christ meets here on the sign out front.”
God bless your congregation and it’s efforts.
There is no requirement in the Bible that says the church must use the name "church of Christ." There are a variety of names for church used in the New Testament. What is common about them is that they each give recognition to Christ, who is our Lord.
While that is the case, experience tells me that it is very rare to find congregations which actually stay with Bible but who don't associate themselves with the other churches of Christ. There has to be some difference; otherwise, why bother going to worship at another place? I suspect that if you looked into the doctrine of the group, you find numerous variations from the teachings of God. It is in those differences that I would begin. "I was looking up what the congregation you attend believes. I didn't realize that you think ____, especially when God said _____." If they deny that that is what they believe, then ask if attending that group doesn't mean they are saying they support their teachings, at least for the most part.
What you want is an open dialogue about what is right and wrong. By saying you looked into their concerns and didn't dismiss them out of hand. You don't want it to decay into an "us versus them" conversation. So don't pile a hundred problems up on them at once. Stick to one or two each time you see them. They will either stop wanting to see you or you'll open their eyes to things they did not want to see before.
"But avoid foolish and ignorant disputes, knowing that they generate strife. And a servant of the Lord must not quarrel but be gentle to all, able to teach, patient, in humility correcting those who are in opposition, if God perhaps will grant them repentance, so that they may know the truth, and that they may come to their senses and escape the snare of the devil, having been taken captive by him to do his will. (II Timothy 2:23-26).
Thanks and have a blessed week.