Atheists complain that they are distrusted. Being atheists, they think that's unfair. Sheer prejudice.
But here's the problem: it's not directly about morality. There are atheists who inconsistently believe in morality. So it's not that they can't be trusted because they are immoral or amoral–although some certainly are. And, indeed, atheists are far more likely to deny moral realism than Christians. So the odds are that they are less trustworthy in that respect.
But that's not the main thing. It's less about morality than mortality. If you think this life is all there is, then are you going to do the right thing even if that puts you at personal risk? I'm not saying you don't have brave atheists, but from the standpoint of mortality, isn't that foolhardy?
To take a cliche example, suppose you're gentile and your best friend is Jewish. But then the Nazis come to power. You still want to be his friend. But there's now a conflict between self-interest and altruism. Are you prepared to risk your life or freedom to remain his friend?
From a secular standpoint, isn't that irrational? So that has an indirect effect on your commitment to morality. In a pinch, can your Jewish friend trust you to watch his back? Or is the price too high? In normal times, your friendship isn't costly. Indeed, your friendship is mutually agreeable. But now that friendship is politically dangerous. If this life is all there is, will you hazard your life or freedom to protect him? Or will you protect yourself?
The acid test of friendship is taking a risk–even a grave risk–for your friends. That's a gamble. And if you can't afford to lose the bet, you can't be a real friend, you can't be a friend when it matters most. When the stakes are high, that's why he needs a friend–and that's when the stakes are too high for you to be his friend. It isn't safe to be around him.