That I applaud him for his stance on smoking says that I share and support his belief that smoking is bad. That I applaud someone on their belief says that I share and support what they believe, be it that there is a god or that there isn't.Wouldn't this be the relation?
"I would applaud him for his stance on smoking" = "I applaud him for his viewpoints" or "I applaud him for his stance on belief"
It seems a bit tricky to say "I applaud him for his beliefs" because it can be ambiguous, as if he has a belief in a God.
If they are going to turn it on its head to say that they have no stance, no belief, no viewpoint, then I literally have nothing to applaud. Then, it's certainly not atheism that I am applauding.