In particular I'm thinking of things like Dylan or CLOS. When people from the more typical OOP backgrounds see stuff like that often their heads explode.
I recently got into an argument with some coworkers over type classes. My argument was that it all made sense when viewed from the Dylan/CLOS/S4/etc lens, and that this was very much OOP, just not what they were used to. Many of them weren't buying what I was selling, but IMO they were using too strict a definition of OOP.
I tried CLOS, not a fan to be honest. OOP (or functional) isn't a very well-defined concept... I like what languages such as Ceylon, C# or Julia (to an extent) are doing - solid support for both OOP and functional styles. Because you typically need both, some problems are more readable and natural in OOP, others in FP.
On that I fully agree. And going back to your statement that it isn't a very well-defined concept, I think that the two concepts aren't nearly as orthogonal as many would have you believe, it's just that the ways that the two communities have solved similar problems over the years appear to be alien to each other.
You read mostly right. But the OOP language I like the most is Ceylon (it also has a first-class support for the functional paradigm).