Although the genders are treated equally in this regard now, only one citizen parent is required to confer citizenship at birth.
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SCOTUS ruling (Minor v Happersett) used the plural of ‘parent’ in defining natural born citizen. And there is a back story of Pres. Garfield appointing a USSC justice who later ruled on Garfield’s status as natural born citizen who had only 1 citizen parent at his birth, although his father became naturalized after he was born. And there was no polygamy involved as in Obama’s case. Here’s the link -
http://www.fourwinds10.com/siterun_data/government/us_constitution/news.php?q=1308252582
Which, incidentally, supports my assertion that the terms 'native born' and 'natural born' are used interchangeably (this time in Vattel).
However, to address your claim of multiple parents, in every case cited at the link you provided, the use of 'parents' refers to multiple children's parents and there is no indication that both parents of each individual are meant. And only in the blogger's own interpretation is the construction of multiple parents of an individual; never in the actual text cited to support the blogger's claims.
Do you believe that all children spring from the same two parents? Or is it possible that they are talking about multiple citizenship-conferring individuals that might never have met, never mind procreated together?