Most martial arts have some type of spiritual basis, some stronger than others. This is usually a connection with a person's inner self rather than with some outside deity. 

Some martial arts have a strong religious connection while other have no religious connection or have virtually eliminated any previous religious connection. Even for some marital arts that had strong religious connections in the past, the modern practices of the arts have eliminated the religious connections and instead concentrate on the scientific combat aspects.

Most martial arts in the United States, including Taekwondo, do not have any religious connection but that does not prevent some zealots from finding a connection. They find what they believe is evidence of the martial arts being some sinister Eastern plan to undermine Western religions. There is no way to argue with zealots, they believe what the believe and they reject anything that challenges their beliefs.

I once had a Christian family that had been attending classes for months. Then one night while teaching the Dan-gun pattern, I told about the legend of Tan-gun when in ancient times animals could speak and a bear turned into a woman who gave birth to Dan-gun. Somehow this offended the family, so they stopped training. American legend did not seem to bother them but Korean legends offended them.  They that it is a fact that Eve was created from dirt and that a serpent spoke to her, but they are offended by a legend that does not purport to be factual.

Some people may have questions about how their training in Taekwondo may conflict with their religious beliefs. The following link has numerous articles on how the martial arts relate to Christian dogma. A search of the Internet should find other sites that deal with the relationship between the martial arts and other religions.

A Christian Response to the Martial Arts