The precise/pedantic lisper may insist that since Lisp stands for List Processing and Lists are chains of cons cells and since Clojure doesn't have cons cells for the built-in lists, then Clojure is not a Lisp.
If, however, you view lisp (lower case) as a family of homo-iconic languages that use s-expressions, then Clojure happily fits under that umbrella.
The trick is to pay close attention to whether the person is talking about a Lisp (ANSI Common Lisp implementation) or a lisp (the family). Sometimes people say "lisp" when they are talking about "Lisp", which can cause some confusion.
=> (class (read-string "(some list)"))
clojure.lang.PersistentList
They are written in Java, and implement a bunch of interfaces, so the implementation looks complicated, but they are basically just classes with _first and _rest fields.https://github.com/clojure/clojure/blob/master/src/jvm/cloju...
Clojure has "sequences" or "seqs", which are semantically the closest to what lispers mean by a "list"—but also "vectors," denoted by square brackets, "maps," denoted by curly brackets, and "sets", denoted by curly brackets prefixed with a hash sign. Having these as core data structures violates the Lisp principle of "everything is just a list," and they introduce something other than round parens into the syntax, which looks really weird to those practiced with traditional/conventional Lisps.
For those well-practiced in "true" Lisps, Clojure reads like a very strange hybrid (one might say "corruption") of Lisp and JSON.
The main point is that Lisp actually has decades old established set of data structures, their operators and programming concepts. For example when I would have read a Lisp book, I would find explanations of these core datastructures and operators. In a Clojure book many things work sufficiently differently and also are named differently. In Lisp for example "atom" is a central concept. It's anything which is not a linked list element. In Clojure this word is used to name a completely different concept: a data structure to manage state.
Clojure is more like Lisp, Java, SML put into a blender. The result may have a similar color, some traces of flavor, but other then that it is a new language.
My guess was the only thing that I could really think of. That and the syntax support and integration of non-list datatypes into the core language (e.g. function syntax).