Please explain Leviticus 19:27 and 21:5. Do these verses mean that it is wrong to shave, or cut one's hair?

It was the custom of some heathen nations to cut and trim their beards and hair into particular shapes in honor of some pagan god. The Egyptians, for example, had their hair cut short and in a certain way, so that what remained appeared in the form of a circle surrounding the head (the halo was derived from this). In another instance, a round spot would be shaved off. Both of these forms are indications of sun god worship.

Modern forms of such extremes include: extremely short or even no hair to intimidate (e.g., Nazis, skinheads); strangely cut, colored or spiked hair to intimidate, but also to attract undue attention (e.g., punk rockers, the more recent “Gothic” look, etc.); strangely cut and colored hair at sporting events (a form of idol worship); and many others.

Shaving one’s facial hair and the regular cutting of the hair on one’s head for normal good grooming however, is something totally different and, in fact, should be common practices for Christians. Please read I Corinthians 11:14-15. As with most things, moderation and respect should play the higher role and if in any doubt, “Abstain from all appearance of evil” (I Thes. 5:22).