Why did Greek gods do things that were considered unethical at the time they were worshipped?

Let me illustrate with a parallel.

The original US Constitution, in Article 1, Section 2, Clause 3, rewarded people for owning slaves. It gave extra legislative and voting power to states where slavery was more prevalent.

Yet people still keep this document around? Why would anyone honour a constitution that did something as abominable as that, and drive away people that might otherwise respect it?

I think this is a similar question to the one you've asked. With the Constitution, the answer is of course that you don't get a choice. In the modern day you don't get to just throw away your political system's legal basis. If you're a foreigner visiting the United States, you're governed by its laws and its constitution whether you 'believe' in them or not.

Laws aren't physical realities, but they matter to their people. Similarly with ancient Greek gods. In ancient Greece you didn't get to throw away your political system's religious basis. Religion wasn't about choosing to subscribe to a set of beliefs and values: it was about where you lived, state religion(s), political continuity.

Things like the Argive cult of Hera, the Elian cult of Hades, or the Trojan cult of Athena, had pan-Hellenic prestige, but fundamentally they were attached to particular cities. A Lydian visitor to Delphi would defer to the cult of Apollo because that's how Delphi worked; the idea of not 'believing' in him, or not 'worshipping' him, wouldn't have made any more sense than choosing not to 'believe' in the law of the land. Similarly, a Greek visitor to Libya or Egypt would defer to the cult of Zeus Ammon or Osiris. 'Worshipping' these gods, and the stories about them, wasn't the point.

Ancient Greek gods weren't moral paradigms, and they were never meant to be. They were emblems, avatars, origin stories, for particular people and particular places. Religion was about where you were, and about the mythical stories associated with that spot and with the people who lived there.

Now, gods could stand for particular values, but in a piecemeal way. Persephone represented the possibility of movement between heaven and the underworld; Apollo represented a radio link to the gods; Zeus represented respect for the rights of supplicants and foreigners. But these piecemeal values didn't always work harmoniously, and that's a large part of where the stories of conflict come from. Ancient observers were well aware of their gods' moral failings, and occasionally it did trouble them.

Take a read through Plato's Euthyphro one day. It's one of his shortest and most straightforward dialogues. It strongly emphasises that the traditional gods have their failings, and that they cannot be seen as intrinsically moral entities, precisely because they come into conflict with one another. This troubled Plato -- and, it seems, Socrates -- and it seems that Socrates' search for divinity-as-moral-paradigm is part of what got him into trouble. Bear in mind that looking for a better kind of divinity may sound like a moral thing to do, but (a) it's not much different from wanting to overthrow the constitution and replace it: however good a revolution may sound, the world just doesn't work that way most of the time. (b) Socrates had close links to an oligarchic regime that murdered a significant percentage of Athens' population ... but that's another story, and shall be told another time.

Anyway, stories about gods doing awful things wasn't by itself damaging to the cult of the Olympians. You'll notice that modern countries usually haven't abolished their political systems because of people like Christopher Columbus or Andrew Jackson or Leopold II or even Adolf Hitler.

Incremental change, sure, fine: and that's exactly the kind of development we see in the history of ancient Greek religion too. Philosophers like Plato chose to use Apollo as an emblem of rationality and clarity; that isn't something that was built into the cult of Apollo at Delphi or Delos, it's a reinterpretation of those cults. Allegorists like Theagenes chose to treat gods as metaphors for natural elements and forces like air, water, and wisdom: again, that's an interpretation of the Olympian gods, not the origin of civic religious practices.

The exact meanings of the awful stories you hear about various Greek gods are very diverse, depending on exact historical and ethnic contexts. Sometimes they're not so much about state religion as about artistic or literary interpretations of that religion. I wrote an answer a few months back that talks about how different aspects of gods could come either from civic cult, or artistic iconography, or mythical stories, or other origins.

Most encyclopaedias of Greek myth don't convey that particularity at all well. Virtually every story about these gods has its own origin. But the idea of taking all the various stories and mashing them up into a single myth is an ancient creation too: ancient mythographers had the practice of taking every scrap of information they could find about gods and heroes, from any source they could find, and cramming them all together in one place indiscriminately. The reality wasn't nearly as homogenous as that.

My favourite introduction to the particularity of Greek myths, and just how context-sensitive each story is, is Ken Dowden's 1992 book The uses of Greek mythology, which miraculously has been released on the Internet Archive for free (available in epub, pdf, Kindle, and more). If you find Greek myth interesting, it's a must-read.

Edit: corrected a rather significant 'have' in the 10th paragraph to 'haven't'.