A common enough trope in sci-fi is that intelligent life has been abundant and common throughout the galaxy for billions of years, and that there has been a federation of sorts all that time. Everybody gets along more or less well. Everybody is based on some common biochemistry, at least in the basics. But way back, there were chemical anomalies that led to critters of vastly different capabilities, and that the war to fight these demons off was long and costly enough that the horrors of it have reverberated down through the eons. Rather than good, healthy, proper life based on breathing hydrogen or hydrocarbons, those ancient monsters breathed oxygen. That made them toxic, that made them metabolically far faster, it made them dangerous, it made them evil. Everybody knows this down to their core, even races that haven't developed starflight yet and thus haven't been inducted into the federation. But the war against the oxygen breathers was a mere five billion years ago, so even the youngest races still have some genetic memory of the conflict that set the galaxy on fire. Fortunately, all the oxygen breathers are gone now.
Then the humans show up and say "howdy..."
The federations ideas of morality might well be comprehensible. But their blinding panic and fury will be for reasons the humans cannot hope to comprehend. And it won't be just one alien race out to get us, it'll be an entire galaxy. If it was explained to us, we might understand the motives and morality, but everyone else just loses their minds when they see us, and we never get the first hint of meaningful conversation from *anybody.*
An idea I haven't seen in any depth for utterly alien aliens: life forms based not on regular matter, but dark matter. Their constituent bits interact with the rest of the universe solely with gravity.