Adoption does not matter since a minor cannot legally renounce his citizen. IF Urkel was born a US citizen it cannot be taken away from him until he is of age to renounce it. Laws of other countries do not trump that. It all comes down to whether he was born a natural citizen.
And if it eventuates that he was listed as "Moslem" on any of the aforesaid docs -- BC (as revised at the time of his adoption), or renaturalization documents, or collegiate docs -- then he just has a first-rate political ineligibility as the "secret Moslem" fans cry in unison, "Aha!!"