It's not absolutely necessary for a devoutly religious person look down upon atheists, but the correlation appears to be strong and it would be understandable why. Given how important devoutly religious people regard their faith in their god not only to their lives, but also to matters like morality, it would be a surprise if it weren't difficult for them to regard as fully equal those who reject not only their religion and their theism, but also that religion and theism are necessary or even reasonable. Since how Hillary Clinton consistently insists that her religion is very important to her life, atheists should wonder what she really thinks about atheists and atheism.
Clinton stood by her actions in the aftermath of former President Clinton's admission that he had an affair, including presumably her decision to stay in the marriage. "I am very grateful that I had a grounding in faith that gave me the courage and the strength to do what I thought was right, regardless of what the world thought," Clinton said during a forum where the three leading Democratic presidential candidates talked about faith and values.
"I'm not sure I would have gotten through it without my faith," she said. ...Clinton said she's "been tested in ways that are both publicly known and those that are not so well known or not known at all." She said it's those times when her personal faith and the prayers of others sustain her. "At those moments in time when you are tested, it is absolutely essential that you be grounded in your faith," she said.
If Hillary Clinton believes that her religious faith helped her, that's her business. If Hillary Clinton believes that she needs her religious faith in order to deal with personal crises, that's also her business. I would prefer politicians and presidential candidates who don't need to rely on religion or superstition in order to deal with personal problems, but they don't seem to exist in America. Even wishing for politicians who simply don't think it appropriate to talk about such matters for the sake of getting more votes is probably asking too much.
Where I absolutely have to draw the line, however, is when politicians make the clear and deliberate implication that everyone needs religious faith in order to deal with personal problems. That's precisely what Hillary Clinton does when she says that "it is absolutely essential that you be grounded in your faith." It's theoretically possible that the "you" in this sentence is only meant to refer to herself or to religious believers like herself, but that seems to me to be stretching it a bit.
It's much more natural, I think, to read the "you" as a reference to people in general. If she had said that "At times when you are thirsty, it is absolutely essential that you have enough clean drinking water," wouldn't it be obvious that she's referring to everyone who gets thirsty? Similarly, the statement above is, to me, obviously referring to everyone who is "tested," i.e. experiences serious personal crises. It wasn't enough for her to say that religion was important to her, she had to go on to insist that religion has to be important to everyone.
The implication is that those who are not "grounded" in religious faith simply aren't able to cope with such problems - which means all secular atheists and secular theists (people who believe in the existence of some god, but don't have any sort of religion structured around this belief). That, in my opinion, is bigotry. In fact, it's dangerously close to the old canard that "there are no atheists in foxholes" because saying that one needs religious faith when you are "tested" is very similar to saying that everyone calls out to God when they are in danger.
If she had said that "it is absolutely essential that you be grounded in your faith in Jesus Christ," thus implying that non-Christians cannot deal with personal crises because they lack Jesus, that would be arrogant and bigoted as well - but most people would immediately recognize it as such. If a presidential candidate had said that "it is absolutely essential that you be grounded in your faith that Muhammad was God's Prophet," can you imagine the outcry from conservative Christians?
I'm sure, though, that unlike others Hillary Clinton didn't intend to express any anti-atheist bigotry and probably never thought about it in those terms. Instead, I think she is probably like many religious theists who are so caught up in the importance of religion and theism to them that they forget that others get by fine without either. Such theists never stop to imagine that it's possible to live good, productive, happy lives without all of the assumptions and beliefs which they personally take for granted and/or consider most important.
That would mean that this comment isn't so much an expression of bigotry as it is a personal failure of imagination and a sign of possibly being locked in one's own perspective to the exclusion of all others. That's not a good quality for someone with presidential aspirations, but perhaps not as bad as outright bigotry.