No. Tribal marriages were legal and binding and you cannot play mix and match between the three legal types of marriage. There is no evidence that BHO Sr. was ever a Muslim (he was a professed atheist socialist) or that any of his three marriages were Muslim or that any of his wives were Muslim. Only multiple Muslim marriages would be permissable and only within Kenya...not in HI where bigamy of any kind is illegal.
You quoted from the 1948 BNA:
"5.—(1) Subject to the provisions of this section, a person born after the commencement of this Act shall be a citizen of the United Kingdom and Colonies by descent if his father is a citizen of the United Kingdom and Colonies at the time of the birth"
But this does not apply to Barry if his parents bigamous marriage made him illegitimate. UK does not recognize any marriage that was illegal where performed such as alleged Muslim plural marriages if performed where illegal.
Under the 1948 BNA only legitimate children of a UK subject father automatically become UK subjects at birth. You appear to have missed the following passage from my prior comment which would exclude little Barry from the passage you quoted:
“(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
If a child is born out of wedlock within the UK and its territories, but the father was an alien of the UK, then your argument applies. You are missing the key concept in section 23, which discusses legitimated children.
Do you understand the difference between legitimate and legitimated?