I didn’t mean Constitution — went back to clarify it this morning but couldn’t get in FR. The Constitution has the basic rules and then laws have clarified who can be native born.
A person whose father was a foreigner visiting the country, a father who returned to that foreign country and served as a official in the foreign government -- the child is definitely NOT "natural born" to allegiance. By circumstance of the father, the son's allegiances derived from his birth are dual.
In Obama's case the dual allegiance is clear -- Obama when back to Kenya to join to his father's family and affairs. Obama campaigned for and advised his father's brother, running for office in Kenya.
Yes, a US citizen, a native-born citizen, can have dual allegiances and run for any office. Any office except the Presidency and Vice-Presidency.