Essentially, the message of this meme is virtually correct; I would go much further than that. While they can indeed visit, they cannot be members of the church if they do not repent of their sins and give their lives to Christ alone.
With that said, I wonder if by the use of the template above, are you fulfilling or violating Colossians 4:6?
An unregenerate sinner, by his or her nature, cannot obey God (Romans 8:6-7) anymore than can a sinner who doesn't know Christ (John 10:27-30). Both the former and the latter can obey the 10 commandments, after all, unbelieving Jews does so all the time and yet none of them are going to heaven (Romans 10:1-4).
But if they resolve to live a life of repentance, and give their lives to Christ, then they are saved.
And when they are saved, they are changed as they receive a new nature (2 Corinthians 5:17) the fruits of the believer will manifest itself in their lives. If they do not, but pretend to be Christians, then eventually they will eventually leave (1 John 2:19). Their hidden, unrepentant life will eventually be exposed.