It is not purely functional. The main difference from r7rs scheme is that lists are immutable, but that has been the idiomatic way in scheme anyway.

It even supports generalised set!.

LispKit Lisp is purely functional [1].

I did read the GitHub announcement but was just trying to make the point that re-using names of software packages isn't a good idea, thanks for providing an example.

[1] https://en.wikipedia.org/wiki/Lispkit_Lisp

Can you still put mutable cells (refs) inside these lists?

I doubt that would be an issue. I think it has more to do about the correctness of the list implementation. In r5rs you can mutate a list from underneath your own feet, and ensuring a correct program state requires some extra checks that may slow list operations down.