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According to Wikipedia, Halaal food is restricted to being anything that is not:
Pork meat (i.e. flesh of swine)[Qur'an 2:173]Blood[Qur'an 2:173]
Animals slaughtered in the name of anyone but Allah (God) (there are debates regarding the permissibility of meat slaughtered by Jews, i.e., kosher meat).[Qur'an 2:173]
Carrion[Qur'an 5:3]
"Fanged beasts of prey" as per the Sunnah, usually simplified to all carnivorous animals, with the exception of most fish and sea animals[citation needed]
Anything not on that list is perfectly permissable.
Obama has been known to eat pork. Specifically he has been witnessed eating pork sausages.
There would be no requirement for him to eat sausages in order to hide his religion - he could order a rump steak and eat it with a soured cream sauce and most Americans would assume that he is proving that he isn't a Muslim, because a lot of Americans don't know the difference between Kosher and Halaal.
He is no stealth Muslim. If he was anything he would be a stealth atheist - but then, that is just wishful thinking on my part.