MENSTRUAL BLOOD
The Canons of Dionysius (Archbishop Dionysios of Alexandria), Canon 2, 247 AD
What makes sense is that a menstruating woman at a sex orgy would get messy blood all over the place:
http://www.womenpriests.org/traditio/can_dion.asp, The Canons of Dionysius: AD 247:
Canon 2. “Menstruous women ought not to come to the Holy Table, or touch the Holy of Holies, nor to churches, but pray elsewhere.”
http://www.stnina.org/journal/art/3.2.2, Orthodox Women and Pastoral Praxis, “Women and ‘Uncleanness’”:
The first is canon 2 of Archbishop Dionysios of Alexandria, a pupil of Origen, who lived during the mid-third century. Apparently answering the question asked of him, Dionysios states in his canon: "Menstruous women ought not to come to the Holy Table, or touch the Holy of Holies, nor come to churches, but pray elsewhere."12 He gives no explanation for his observation.
…
12. Canonical Letter of Dionysios of Alexandria in The Nicene and Post Nicene Fathers (henceforth NPNF) (Grand Rapids, Mich.: Eerdmanns, 1956), p. 600. However, in Canon 4 he leaves it up to the discretion of the man whether or not to commune, after he had experienced "involuntary nocturnal pollutions."
Same in the Old Testament:
Sexualia: From Prehistory to Cyberspace, Bishop / Osthelder, 2001, p. 37, “Menstruation”:

Eros and Ethos: A Comparative Study of Catholic, Jewish and Protestant Sex Behavior, Lopez, 1979, p. 21, “Religious Influence on Sex Behavior”:

It sounds like the reason women were shunned during their menstrual period was for them to avoid sex.
Leviticus 15 (KJV):
[1] And the LORD spake unto Moses and to Aaron,
saying,
[2] Speak unto the children of Israel, and say unto them, When any man
hath a running issue out of his flesh, because of his issue he is unclean.
[3] And this shall be his uncleanness in his issue: whether his flesh
run with his issue, or his flesh be stopped from his issue, it is his
uncleanness.
[4] Every bed, whereon he lieth
that hath the issue, is unclean: and every thing, whereon he sitteth, shall be
unclean.
[5] And whosoever toucheth his bed
shall wash his clothes, and bathe himself in water, and be unclean until the
even.
[6] And he that sitteth on any thing whereon he sat that hath the issue
shall wash his clothes, and bathe himself in water, and be unclean until the
even.
[7] And he that toucheth the flesh of him that hath the issue shall wash
his clothes, and bathe himself in water, and be unclean until the even.
[8] And if he that hath the issue spit upon him that is clean; then he
shall wash his clothes, and bathe himself in water, and be unclean until the
even.
[9] And what saddle soever he rideth upon that hath the issue shall be
unclean.
[10] And whosoever toucheth any thing that was under him shall be
unclean until the even: and he that beareth any of those things shall wash his
clothes, and bathe himself in water, and be unclean until the even.
[11] And whomsoever he toucheth that hath the issue, and hath not rinsed
his hands in water, he shall wash his clothes, and bathe himself in water, and
be unclean until the even.
[12] And the vessel of earth, that he toucheth which hath the issue,
shall be broken: and every vessel of wood shall be rinsed in water.
[13] And when he that hath an issue is cleansed of his issue; then he
shall number to himself seven days for his cleansing, and wash his clothes, and
bathe his flesh in running water, and shall be clean.
[14] And on the eighth day he shall take to him two turtledoves, or two
young pigeons, and come before the LORD unto the door of the tabernacle of the
congregation, and give them unto the priest:
[15] And the priest shall offer them, the one for a sin offering, and
the other for a burnt offering; and the priest shall make an atonement for him
before the LORD for his issue.
[16] And if any man's seed of copulation
go out from him, then he shall wash all his flesh in water, and be unclean
until the even.
[17] And every garment, and every skin, whereon is the seed of copulation, shall be washed with
water, and be unclean until the even.
[18] The woman also with whom man shall
lie with seed of copulation, they shall both bathe themselves in water,
and be unclean until the even.
[19] And if a woman have an
issue, and her issue in her flesh be blood,
she shall be put apart seven days: and whosoever toucheth
her shall be unclean until the even.
[20] And every thing that she lieth
upon in her separation shall be unclean: every thing also that she sitteth upon
shall be unclean.
[21] And whosoever toucheth her bed shall wash his clothes, and bathe himself
in water, and be unclean until the even.
[22] And whosoever toucheth any
thing that she sat upon shall wash his clothes, and bathe himself in water, and
be unclean until the even.
[23] And if it be on her bed, or on any thing whereon she sitteth, when
he toucheth it, he shall be unclean until the even.
[24] And if any man lie with her at all, and her flowers be upon him, he
shall be unclean seven days; and all the bed
whereon he lieth shall be unclean.
[25] And if a woman have an
issue of her blood many days out of the
time of her separation, or if it run beyond the time of her separation; all the
days of the issue of her uncleanness shall be as the days of her separation:
she shall be unclean.
[26] Every bed whereon she lieth all the days of her
issue shall be unto her as the bed of
her separation: and whatsoever she sitteth upon shall be unclean, as the
uncleanness of her separation.
[27] And whosoever toucheth
those things shall be unclean, and shall wash his clothes, and bathe himself in
water, and be unclean until the even.
[28] But if she be cleansed of
her issue, then she shall number to herself seven days, and after that she
shall be clean.
[29] And on the eighth day she shall take unto her two turtles, or two
young pigeons, and bring them unto the priest, to the door of the tabernacle of
the congregation.
[30] And the priest shall offer the one for a sin offering, and the
other for a burnt offering; and the priest shall make an atonement for her
before the LORD for the issue of her uncleanness.
[31] Thus shall ye separate the children of Israel from their
uncleanness; that they die not in their uncleanness, when they defile my
tabernacle that is among them.
[32] This is the law of him that hath an issue, and of him whose seed goeth
from him, and is defiled therewith;
[33] And of her that is sick of her flowers, and of him that hath an
issue, of the man, and of the woman, and of him that lieth with her that is
unclean.
As you can see, no one wants her menstrual blood on them, because it’s literally “unclean.”