Any registered voter who meets his or her state's requirements to vote has the right to cast a ballot at the polls on Election Day, regardless of what he or she is wearing. Wearing a piece of Obama clothing will not keep you from voting.
Political experts are already calling deceptive email rumors to the contrary for what they are - shadowy, harmful voter suppression techniques:

Larry Sabato, director of the University of Virginia Center for Politics, called the barrage of e-mails "a dirty trick" aimed at suppressing Democratic voters.
"It is terribly wrong," Sabato said. "Tragically, it is all too common. One would hope the people responsible could be caught and prosecuted."

It is true that in some states, wearing campaign gear is not allowed at the polls - but no matter what, your vote cannot be taken away from you. At most you will have to take off a button or put a jacket over a T-shirt.

Since different states have different rules, you should direct any questions to your state's secretary of state or county election officials. Election officials in Kentucky, Pennsylvania, and North Carolina have already issued statements reaffirming that wearing campaign gear will not keep anyone from voting.