Checked Google and there are some links that remark that Obama does not celebrate Christmas nor does he give birthday gifts to the girls..so the opinion of the authors is that there is some Muslim in him as the Muslims do not give gifts for birthdays and do not celebrate the Christmas holiday in any way. So maybe there is someting to it. I did not find anything on Snopes yet.
Jehovah's Witness's don't celebrate Christmas either. That is not the point. Obama is dangerous because of his socialist bent. The rest is a non issue.
Well maybe The Muslim part is.
Muslim do exchange gifts (and pretty expensive ones when they can afford!).
They do not celebrate Christmas as much as Christians do not celebrate Ramadhan or Eid. I am Christians and certainly I do not celebrate Christmas giving big gifts to my kids. BTW, on their birthdays too they get no party but only symbolic presents. When they perform well in school and are well behaved in everyday life, then we reward them with HUGE gifts ! I guess anybody can raise their kids as they want and it is nobody business (even when you are a president).