Beliefs are still important I think. Perhaps the two options you gave of belief and witholding judgment are morally equivalent given e.g. the Kalama Sutta. But rejecting rebirth is clearly stated as a wrong view, holding wrong view is an unwholesome mental action (i.e. bad kamma), and unwholesome actions lead to a bad rebirth.
And how is unprincipled and immoral conduct threefold by way of mind? It’s when a certain person is covetous. They covet the wealth and belongings of others: ‘Oh, if only their belongings were mine!’
They have ill will and hateful intentions: ‘May these sentient beings be killed, slaughtered, slain, destroyed, or annihilated!’
They have wrong view. Their perspective is distorted: ‘There’s no meaning in giving, sacrifice, or offerings. There’s no fruit or result of good and bad deeds. There’s no afterlife. There’s no obligation to mother and father. No beings are reborn spontaneously. And there’s no ascetic or brahmin who is well attained and practiced, and who describes the afterlife after realizing it with their own insight.’ This is how unprincipled and immoral conduct is threefold by way of mind.
That’s how unprincipled and immoral conduct is the reason why some sentient beings, when their body breaks up, after death, are reborn in a place of loss, a bad place, the underworld, hell.
I’m quite sure you know all this so this post is meant for more general consumption.