Christians who belong to a denomination usually accept people can be true believers in the true church without belonging to their denomination.
Members of a denomination will usually say that Christians and churches outside their denomination can have as much of grace, and be as spiritually blessed, and be as much the body of Christ, as those who belong to their denomination. They will feel the same way about Christians and churches who are outside all denominations. It is accepted that churches and Christians don't have to be under a denominational umbrella in order to be Christ's body and receive the full blessing of grace.
The difference between those who are "simply Christians", and those who belong to a denomination, is that "simply Christians" have faith in the sufficiency of God-given things, and add nothing to them. There are two principles worth mentioning here, before we look at some of these God-given things. You might call these principles "simple arithmetic" for the church:
The first principle is that you cannot add anything to everything. If what God has given is all-sufficient, then how can a denomination add something to improve it? We all know that if you add to what is perfect, you make it imperfect.
The second principle is that you cannot divide something by nothing. You have to have something by which to divide, and all denominations do. A truly undenominational church would have nothing but what God has given, and so would have nothing by which to divide God's people.
With these principles in mind, I would like to look now at three things that would be true of those who are truly "simply Christians" —firstly the name they wear, secondly the creed they follow, and thirdly their origin.
A name with God's authority. It was prophesied that Christians would "be called by a new name, which the mouth of the Lord shall designate" (Isaiah 62:2). Very few denominations claim that their name fulfills this prophecy!
A name that unites. Surely there is uniting power in the name God designates for his people, and we can "glorify God in this name" (1Peter 4:16). Using only a name designated by God, we contribute to fulfilling the Lord's prayer that his followers be one (John 17:21). The disciples were called Christians (Acts 11:26).
A non-denominational name. The Holy Spirit has used other terms besides "Christians" to designate Christ's followers, but none of these is a denominational name. Some examples are:
A creed (from Latin credo "I believe") is a form of words that members of a denomination consent to and "confess". Undenominational Christians are content with the acknowledgement of Christ that he requires and reciprocates (Luke 12:8). This "good confession" (1Timothy 6:12) is surely good enough.
To the extent that one is bound to a denominational creed, to that extent one is inhibited from examining the scriptures to find truth, and using the scriptures as one's authority or rule of faith. The scriptures are able (powerful) to make one wise unto salvation and completely equipped for every good work (2Timothy 3:14-17).
God's word is the seed of the kingdom (Luke 8:5,11) and the "sword of the Spirit" (Hebrews 4:12). This cannot be said of a denomination’s creed.
Prophecy said that the true church would begin in Jerusalem (Isaiah 2:1-4, Micah 4:1-2). Jesus confirmed that his church would originate from Jerusalem (Luke 24:46-49 Acts 1:4-8). If a congregation of Christians is really undenominational, then surely it originates from the first church, the church formed in Jerusalem about AD33, as recorded in Acts chapter 2.
An undenominational church is formed by replicating the church pattern instituted by Jesus Christ. This was the pattern on which he formed the church in Jerusalem —one of his first acts after taking the throne in heaven.
This means much more than just using the same "blueprint". It means receiving the same "title deed". Jesus is the purchaser and master builder of any church that exists by his authority, and that means any church formed according to the pattern he has given in the scriptures. Any church that originates in this way must be undenominational, just as the original church in Jerusalem was undenominational.