Question: "Is it acceptable to God for a husband and wife to have sex while the wife is menstruating / having her period?"
Answer: Leviticus 15:19 says, "When a woman has her regular flow of blood, the impurity of her monthly period will last seven days, and anyone who touches her will be unclean till evening." Similarly, Leviticus 15:24 says. "If a man lies with her and her monthly flow touches him, he will be unclean for seven days; any bed he lies on will be unclean." Finally, Leviticus 20:18 declares, "If a man lies with a woman during her monthly period and has sexual relations with her, he has exposed the source of her flow, and she has also uncovered it. Both of them must be cut off from their people." As a result of these Scriptures, some hold that a married couple should not have sex while the wife is having her period.
The problem with this view is that if the Scriptures are applied consistently, even touching a woman who is having her menstrual flow would be forbidden. Further, according to Leviticus 15:20-23, even touching something that the woman has also touched would be forbidden. Do these laws apply to us today? No, they do not. Why? It is important to remember the purpose of the Old Testament laws concerning blood. In the sacrificial system, blood was sacred (Leviticus 17:11). A woman's "uncleanness" during her period was symbolic of the value placed on blood. As a result, contact with a woman who was having her period was forbidden.
Christians today are not under the Old Testament ceremonial law (Romans 10:4; Galatians 3:24-26; Ephesians 2:15). There no longer is a sacrificial system. Jesus' blood sacrifice paid the penalty for sins once and for all. The Levitical ceremonial laws do not apply today. There is no biblical reason why a married couple cannot have sex during the wife's period. Some doctors do not recommend it from a medical perspective, but there are no proven "dangers" of having sexual intercourse during a woman's period. Usually women have no desire to have sexual relations during their period, so that is definitely another thing to consider. Basically, this issue must be decided by a husband and wife in the spirit of "mutual consent" as 1 Corinthians 7:5 describes.