The New Church and the Church of New Jerusalem are alternate names for Swedenborgianism. This group, which has been around since the late 1700s, is well outside of orthodox Christianity in its beliefs and can definitely be labeled as a cult.
Swedenborgianism bases its teachings on the writings of Emanuel Swedenborg, who was born in Stockholm, Sweden, in 1688. His training was in science, but sometime around 1750 he had a vision in which he believed God came to him and declared him to be God’s personal messenger of new revelation. Further encounters with God and other beings in the spiritual realm he traveled to were the basis for his many writings.
These writings include teachings such as: God has many names, depending on the beliefs/religion of the individual; the Holy Spirit is not God; the Trinity does not exist; Jesus Christ’s death did not atone for our sin; salvation comes by practicing what you believe, whatever religion it might be; the afterlife is spiritual, but dependent on how well you lived in your physical body.
None of these teachings are compatible with biblical Christianity. The God of the Bible is the only true God (Exodus 3:13-14; Isaiah 43:10). All other gods are idols; creations of man (Exodus 20:4-5). The Holy Spirit is definitely declared to be God in the Bible (Acts 5:3-4), as is Jesus Christ (John 1:1, 14) and God the Father (Philippians 1:2); the Trinity is a valid, biblical reality. The Bible is also very clear on Jesus’ vicarious atonement of our sin (1 Peter 2:24; 1 John 2:2), and that it is only through belief in Jesus’ life, death, and resurrection that salvation is possible (John 14:6; 1 Corinthians 15:1-4). The after-life will be experienced in one of two places—heaven or hell—and that in a physical body (Revelation 22).
Swedenborgianism, and its churches by whatever name they might be called, are as far outside historical, biblical Christianity as a group can get. Although they might claim to base their teachings on the Bible, every teaching is tainted by heresy, confusion, and sometimes lunacy.