Which word is best described as "not connected with religious or spiritual matters"?

The term that best describes "not connected with religious or spiritual matters" is secular. This word specifically refers to things that are non-religious, pertaining to the worldly, or related to the physical realm rather than the spiritual one. It is often used to describe concepts, institutions, or individuals that operate independently from religious frameworks.

In contrast, sanctimonious refers to acting superior or holier than others, often in a pretentious way regarding one's moral or religious beliefs. Severance generally pertains to the act of cutting off or separating, which does not relate to religion or spirituality directly. Skeptical conveys doubt or questioning attitude, which might apply in a religious context but does not specifically reflect the aspect of being non-religious as secular does. Therefore, the best fit for the description provided is indeed secular.