I’m not saying that your LDOs are fried. What I am saying is that some LDOs don’t take too kindly on not having the company of some nice caps.
What just caught my eye is that the datasheet specifies ceramic non-polar caps. That seems a bit weird. Just drawing a non-polar would have made sense, but specifying that it is a ceramic is strange. Using a ceramic makes sense, I mean there are 5 times the ceramic 1uF caps on digikey than there are electrolytics, but it should be technologically agnostic… I’d probably try to get some 1uF ceramics for testing.