> Clojure is not based on CONSes but you have CAR and CDR they are first and rest.
CAR and CDR are operations on conses, so you can't have them without conses; that's like having sqrt without numbers. Lisp has FIRST and REST for operating on lists, and so does Clojure. Lisp also has CAR and CDR for operating on conses, but as Clojure doesn't have conses, it doesn't have CAR and CDR, either.
> Processors are no more based on accumulator and decrement registers
CAR and CDR were named for 'contents of address part of register' and 'contents of decrement part of register', not anything about accumulator or decrement registers. I'm not sure where you heard that processors don't have accumulators anymore, but that's definitely not true. The reason Clojure doesn't have CAR and CDR doesn't have anything to do with obsolete processors, though.
> Clojure is based on immutability like Scheme
Scheme is not based on immutability.
> CL is often used in a mutable way (see the shameful f-set).
Do you mean SETF? FSet[0] is an immutable data structure library for Common Lisp. A lot of Schemes have SETF, too, by the way, there's even an SRFI[1]. But SETF is just so that you can have one generic assignment operator; standard Scheme has plenty of commonly-used, destructive assignment operators like set-car!, set-cdr!, vector-set!, etc.
0: https://common-lisp.net/project/fset/Site/FSet-Tutorial.html
1: https://srfi.schemers.org/srfi-17/srfi-17.html