How much differently was religion perceived so that they were able to justify worshipping beings which are so utterly reprehensible in behavior?
I think you miss something crucial in this assessment:
This isn’t perfect but I can give you some context you should keep in mind
Most of what we have left from those days are the stories, which, admittedly don’t shine the gods in a great light, but back then, there was a TON more than just that.
Gods were a part of everyday life in big ways, from rituals, festivals, dedicated places in homes (such as the fireplace being reserved for the worship of Hestia) and so on. So when the Greeks (and others) thought about their deity’s, it wasn’t the legends and myths that would most easily come to mind, it might be that good harvest Demeter blessed you with this year, or the favorable winds for trading ships, or good weather, or the music or wine you had to thank them for, or any number of things. It goes on forever.
Nowadays all we really have to look to for information are these old myths, and the few archeological bits and pieces that are left behind, so what we know and see is but a fraction of what the average Ancient Greek would have had to reference when thinking of any particular god.
As for these stories, we should keep in mind the different morality of those days, and even taking that into account it’s often easier to identify with things that have human flaws and characteristics. Lots of these myths were created to explain something in the world, or for pure entertainment value, often both.
So yeah, when we think of Zeus we picture a guy with a nagging wife who can’t stop chasing every woman who catches his eye, and then stands by when his wife punishes the poor girl severely. But for the Greeks, they would think of the lord of their world, protecting them from misfortune and dealing out justice to wrongdoers. And his wife? The nagging Hera who is often so unlikable in the myths? Well she was the patron and protector of marriage, standing by women in childbirth, holding her chaotic family together in times of strife. In the myths, she is almost never nice, but in those days, every happy marriage or successful birth was cause to celebrate her.
With the passage of time we lose this context, and all we are left with are the bare stories, so it’s no wonder all the gods look terrible to us, because for a lot of us, religion looks like an all powerful, all knowing, all loving creator, who watches over us and is ready to forgive. So when we look at gods that have very human flaws and make mistakes left and right, and most certainly are not all knowing and all powerful, it looks crazy.