It does not appear to me that plural marriages were legal in UK Colonial Kenya, especially in the predominantly non-Muslim Lake Victoria part of Kenya where Obama Sr and Kezia were from. The Kezia marriage was a tribal, not Muslim marriage.
The part of Kenya that is predominantly Muslim is in the former Kenya Coast Province (including Mombasa) which was leased by the UK from the Sultan of Zanzibar at the time Obama II was born.
Note that the 1948 BNA explicitly excludes illegitimate children from receiving UK citizenship (UK Kenya Colony citizenship in this case).
It is not at all clear what BHO II's citizenship status would be if he was born in Kenya to the bigamously married white second wife of BHO Sr. Unfortunately it appears to me that only litigation in the UK and HI, given full access to Kenya and HI records and witnesses surrounding the birth, could resolve his citizenship status.
The Kenya Marriage Act specifically makes plural marriage illegal after tribal marriage and even for Muslims specifically mentioning them.
• See Kenya Marriage Act of 1902 paragraph #49:
49. Whoever contracts a marriage under this Act, being at the time married in accordance with native law or custom or in accordance with Mohammedan law to any person other than the person with whom such marriage is contracted, shall be guilty of an offence and liable to imprisonment for a term not exceeding five years.
kenyalaw.org/family/statutes/...?file=The+marriage+act.pdf
• BNA of 1948 Legitimation of persons born out of wedlock:
23.—(1) A person born out of wedlock and legitimated by the subsequent marriage of his parents shall, as from the date of the marriage or of the commencement of this Act, whichever is later, be treated, for the purpose of determining whether he is a citizen of the United Kingdom and Colonies, or was a British subject immediately before the commencement of this Act, as if he had been born legitimate.
(2) A person shall be deemed for the purposes of this section to have been legitimated by the subsequent marriage of his parents if by the law of the place in which his father was domiciled at the time of the marriage the marriage operated immediately or subsequently to legitimate him, and not otherwise.
http://www.uniset.ca/naty/BNA1948.htm
“(2) Subject to the provisions of section twenty-three of this Act, any reference in this Act to a child shall be construed as a reference to a legitimate child; and the expressions “father”, “ancestor” and “descended” shall be construed accordingly.”
http://www.uniset.ca/naty/BNA1948.htm
http://travel.state.gov/law/info/info_609.html
Birth Abroad to One Citizen and One Alien Parent in Wedlock: A child born abroad to one U.S. citizen parent and one alien parent acquires U.S. citizenship at birth under Section 301(g) INA provided the citizen parent was physically present in the U.S. for the time period required by the law applicable at the time of the child’s birth. (For birth on or after November 14, 1986, a period of five years physical presence, two after the age of fourteen is required. For birth between December 24, 1952 and November 13, 1986, a period of ten years, five after the age of fourteen are required for physical presence in the U.S. to transmit U.S. citizenship to the child.
Birth Abroad Out-of-Wedlock to a U.S. Citizen Mother: A child born abroad out-of-wedlock to a U.S. citizen mother may acquire U.S. citizenship under Section 301(g) INA, as made applicable by Section 309(c) INA if the mother was a U.S. citizen at the time of the child’s birth, and if the mother had previously been physically present in the United States or one of its outlying possessions for a continuous period of one year.
Whether the marriage was legal or not, he is still not a citizen unless his mother filed the necessary forms, by which he could aquire citizenship by naturalization and would not be natural born, still ineligible. His mother did not do that since his grandmother registered his birth fraudulently in Hawaii. (Why complicate matters with legal requirements?)
Without filing the necessary forms for him to gain citizenship, he is still Kenyan and an illegal alien.