Well, this is a little embarrassing: Clojure was one of the biggest influences on Hy in its youth, but that was mostly before I got involved in 2016. I never actually learned Clojure. So hopefully somebody who knows both Hy and Clojure well can answer. I can tell you that at run-time, Hy is essentially Python code, so Hy is more tightly coupled to Python than Clojure is to Java; a better analogy is CoffeeScript's relationship with JavaScript.
I get the impression that Clojure tries to convince the programmer to avoid side-effects a lot more strenuously than Hy does, but it's still not a purely functional language, so I don't know how consequential that is in practice.
Clojure has a good collection library with immutable/persistent data structures, but as a language it allows side effects and has some mechanisms to manage them. It is also possible to call any Java method from Clojure.
Clojure does not work with Java ASTs, it translates into JVM bytecode directly.
I haven't used Hy, but I am the maintainer of a Basilisp which also compiles to Python and aims for reasonably close compatibility with Clojure if you're interested.
Wondering how custom immutable data structures fit in with the Python ecosystem.
Particularly, I know that NumPy arrays and Pandas Series/DataFrames are the popular data structures used in research computing in Python (for Statistics, Data Science, Machine Learning etc.). These data structures afaik are mutable, however (for performance reasons), so at least the aspect of immutability from Clojure cannot be easily integrated with the Python ecosystem.
This project is much younger and used by many fewer people than Hy, so I couldn't really speak to this besides my own opinions. The few who have started using it and contributing seem to just be using it as a way to write Clojure while interacting with popular Python libraries and tools. Kind of the same way that interacting with the Java ecosystem is often more pleasant from Clojure (IMO) than in Java itself.
I've tried to facilitate strong Python interoperability despite the variety of otherwise incompatible features of each language. It's trivial to work with immutable data structures using Clojure idioms and then convert them to Python data structures (as needed) at the boundaries, but the immutable data structures used by Basilisp are also generally compatible with Python's core (read-only) interfaces so that conversion may also not be necessary if you aren't expecting the called function to perform any mutations.
I get the impression that Clojure tries to convince the programmer to avoid side-effects a lot more strenuously than Hy does, but it's still not a purely functional language, so I don't know how consequential that is in practice.