When God gave his Ten Commandments to Moses and Israel, his first one was not, "You should all get along because everybody worships me."
No, he said, "You will have no other gods before me." Of course the other nations had different gods, but Israel also had many gods throughout their history and God judged both them and the other nations for not keeping his command.
This commandment applies today when someone says he worships Jesus but it is not the Jesus as God has revealed him in Scripture. There is a non-Trinitarianism that is attractive called "Modalism." It is attractive because it still calls Jesus God, but it is still not Trinitarian just like Mormonism and Jehovah's Witness beliefs. It states that God the Father, Jesus, and the Holy Spirit are not three members of one Godhead, but that God is only one and that Jesus and the Holy Spirit are just manifestations of him. People who believe this worship a false God because this is not the God of Scripture. The main celebrities that hold this view are the preacher TD Jakes and the singing group Philips, Craig, and Dean, both within Oneness Pentacostalism.
God has to be three distinct people to be a Trinity, and he has to be that way from all eternity. He had no beginning, and will have no end. God the Father, God the Son, and God the Holy Spirit have all existed alongside each other from all eternity. They are all God but they are not all each other.
This is important because for God to be eternally loving he had to have someone to love and to love him back. He has had three persons loving each other always. If God had not had this, then he would be a cold, impersonal god, the same as Allah that the Muslims worship. He would have never sent Jesus to save us and would not love us enough to forgive us of our gross sins that should have killed us.
God has to be three separate persons because Jesus would not have been raised from the dead had God the Spirit not been a separate person from him. If they were all one, then God would be dead and not God.
If they were the same, then there would be no intercessor between God and man for our sins. God would simply be that unknown god beyond the mountains that many pagan tribes worship and who need human intercession. No, but gloriously, God is three separate persons, and we have someone in heaven interceding on our behalf, and we have someone here with us to guide us in the Holy Spirit.
Modalists do not believe in the same Jesus that I believe in and are not true Christians. God can save them, yes, but they are not true believers. Therefore, I will not participate in a church event that has TD Jakes as a speaker, which will happen at my church over the summer. I might sing some PCD songs, but I won't attend their concerts either. Not on purpose. We need to have a right knowledge of the Trinity to properly worship the correct God, and we need to be more discerning about who we recommend as theologians lest we dissolve into apostasy.