I'm sure it can be difficult for people to look at someone like Obama and see bigotry. I'm sure that David Shuster was having a hard time with the term because of a number of reasons: one the scale of rabid bigot to perfectly tolerant, Obama does appear to be more tolerant than where a lot of people are and he's willing to say it, which is more than most politicians have been willing to say; and that he's black makes people think that a victim of discrimination would not themselves discriminate, and so on.
As an atheist, though, I know exactly where John Church is coming from.
I know a lot of people who are basically really nice on the surface, from work or where I live. They are friendly, and are raising children. They care about their communities and all that. But, there is a dark side to them. When there is time between classes we chat or if I run into them around the complex, but you gotta hope that the subject of religion or atheism doesn't come up. Because, ya know, then they drop these bombs, like how important it is for their politicians to believe in god (atheists aren't, apparently, "good enough" to hold public office). Or how you can't be moral without god, or some variation on that theme, like how criminals are reformed by finding god (but not anything else). The other people around them don't hear it as bigotry, because they are believers, too, so they aren't the ones being dumped on. But when an atheist hears language like this, it's like a slap in the face. All these "nice" people... they are bigots, too. If you ask them, do you think atheists ought to be able to do X, they will mostly say, sure, why not. Though, there might be a few exceptions. For instance, if you asked my apartment manager if atheists should legally be able to run for office, she'd say 'yes', but if you asked her if she'd ever vote for an atheist, she'd say no.
If that's not bigotry, what is it? Why won't she vote for an atheist?
According to Merriam-Webster, bigot is defined thusly:
a person obstinately or intolerantly devoted to his or her own opinions and prejudices ; especially : one who regards or treats the members of a group (as a racial or ethnic group) with hatred and intolerance
How is refusing to allow gays to marry not a form of "intolerance"? How is refusing to vote for someone who belongs to a particular group, regardless of their political views, not a form of hatred and prejudice?
Bigots are not all people like members of the KKK or Fred Phelps. And I would argue, the "nice" ones are far more destructive, because they blend in, people think their beliefs are acceptable because they are mainstream, and they "seem" reasonable to outsiders. But I would argue that the "nice" bigots are far more dangerous because there are more of them, and they are harder to argue against. Sometimes the only way to draw attention to the problem is by using strong language, to call a spade a spade. It suffers a bit from a kind of black-and-white thinking, but as a rhetorical device, it's necessary sometimes.
Though it's true, given the choice between living in a culture like Saudi Arabia vs. living in the American South, I'll pick the American South... but that doesn't make the prevailing views there about gays or atheists in the slightest acceptable.