This question touches on an area where our stand is somewhat different than that of many other believers in Christ. So, first of all, we would like to state that nothing that follows is meant to condemn anyone. We do not consider ourselves better than other believers who also love the Lord Jesus. But we have, we believe, seen something of God's purpose for the church and we are doing our best to be faithful to what the Lord has shown us. We respect the fact that there are many other believers who are just as faithful to what the Lord has shown them even though their views are somewhat different than ours.
This does not mean that we consider different beliefs to be all about the same. No, we believe in a living, personal God who formed all things according to His own will and good pleasure. He Himself is the truth, the reality, of the universe. The more our living and working are according to His desire, the more eternal value they have. What we do mean is that we are not the judges of others. Only the Lord knows how to judge all men with justice. When He comes the real value of each ones work will be made manifest. We hope to gain His reward.
Having said that, now let's come to the questions. You asked, "What is your attitude or belief about other denominational and non-denominational churches?" We want to put our answer to this question in context with a brief presentation of our understanding of what the church is. In the New Testament the word "church" is used in two ways. When the Lord Jesus said, "I will build My church" (Matt. 16:16) He was referring to a corporate entity that includes all true believers through all of church history. We call this the universal church. As the Body of Christ it is filled with His life. As the bride of Christ it is being built up to be His counterpart.
There is also a practical aspect to the church. We are limited by time and space. We cannot bring our problems to the New Testament apostles even though we also are members of the Body of Christ. We need a church where we are so that we can participate in it. We call this a local church. Each local church should be an expression of the universal Body of Christ. Our practical participation in the life and building of the Body is in the local churches. There is a book by Watchman Nee called "The Glorious Church" which we enjoy greatly. We recommend it because it presents a far higher view of the church than we can share in a few sentences here.
So what is our attitude or belief about other denominational and non-denominational churches? It is simply that God's purpose for the church cannot be fulfilled as long as all His people are scattered into so many divisions. One of the most pernicious effects of man's fall is that a fallen man is dominated by his self. Thus, throughout church history, it has been extremely difficult for any group of Christians to remain together in harmony for an extended period of time. Conflict always arises sooner or later. Very often the only real solution would be for both parties to deny themselves and take the cross. But the easier solution is for them to separate and each to meet only with those with whom they agree. The result is that everyone goes to the church of their choice and the church remains divided. We see this as great damage to the testimony of Jesus to the world.