First Amendment to the Constitution of the United States of America:

Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.

No elected official, including the President, can—constitutionally—give legal status to his or her religious beliefs. Thus, it does not matter what Obama's feelings about same-sex marriage are; neither he, nor the entire Congress—nor the Supreme Court—can, again, constitutionally—abridge the civil rights of any one group of people.

Obama knows this!

Unfortunately, many other elected officials, and certain (but not all) religious groups, also know this, but refuse to accept it and demand that their religious beliefs prevail, despite the Constitution. They are sufficiently short-sighted that they apparently don't realize that if the constitutional protections are ignored, that very precident could someday backlash on them!

THAT's where the problem lies.

Neither Obama nor anyone else who may disagree with the idea of same-sex marriage, for religious or any other reason, can be fairly accused of being a bigot as long as they neither directly attempt, nor advocate, the passage of unconstitutional laws to have it outlawed.

Case in point:   California's Proposition 9 is unconstitutional, notwithstanding that it got something like 54% of the popular vote. The Constitution protects individuals and groups not just from tyrannical regimes, but from the tyranny of pure democracy (majority rules) as well. The tyranny of a pure democracy can be best exemplified by a lynch mob.

No. Obama is not a "bigot."

Don Firth