According to Mary Pullig Schatz, M.D., it is not true that inverting during menses causes endometriosis. The classic theory was that endometriosis is caused from "retrograde menstruation," in which bits of menstrual endometrium go up the fallopian tubes, lodge in the pelvic cavity, and grow, says Dr. Christiane Northrup, author of Women's Bodies, Women's Wisdom (Bantam Doubleday Dell, 1998). Schatz states that this theory is outdated, and that "it is now known that endometriosis arises from the presence of cells in the pelvic lining that are capable of developing into endometrial-type cells." Schatz does advise against inverting while menstruating, however, because it may lead to vascular congestion: The uterine veins, which are thin, can stretch and partially collapse, while uterine arteries continue to pump more menstrual blood into the uterus. If inversions cause you to bleed more than usual during your period, you may become weak and emotionally vulnerable.
For details, read "A Woman's Balance: Inversions and Menstruation," by Mary Pullig Schatz, M.D., at http://www.iyengar.ch/Deutsch/text_menstruation.htm.
Search our Poses section for asanas that are therapeutic during menstruation.