A number of "paradigms" have come into fashion over the years:
structured programming, object oriented, functional, etc. More will come.
Even after a paradigm falls out of fashion, it can still be good at solving the particular problems that first made it popular.
So for example using OOP for a GUI is still natural. (Most GUI frameworks have a bunch of states modified by messages/events.)
Racket is multi-paradigm. It has a class
system. I rarely use it,
but it's available when an OO approach makes sense for the problem.
Common Lisp has multimethods and CLOS. Clojure has multimethods and Java class interop.
And anyway, basic stateful OOP ~= mutating a variable in a closure:
#lang racket
;; My First Little Object
(define obj
(let ([val #f])
(match-lambda*
[(list) val]
[(list 'double) (set! val (* 2 val))]
[(list v) (set! val v)])))
obj ;#<procedure:obj>
(obj) ;#f
(obj 42)
(obj) ;42
(obj 'double)
(obj) ;84
Is this a great object system? No. But it helps you see that the essence of OOP is encapsulating state with functions that modify it. And you can do this in Lisp, easily.
What I'm getting at: I don't think using Lisp is about being "anti-OOP" or "pro-functional". Instead, it's a great way to play with (and use in production) the basic building blocks of programming. You can explore different paradigms. You can experiment with ideas like "code is data and vice versa".
I don't see Lisp as some sort of spiritual experience. At most, it's like Zen, and satori is the realization that all of these paradigms are just different sides of the same coin. They're all wonderful, and they all suck. The paradigm pointing at the solution, is not the solution. Blah blah blah. :)
My practical advice is, it sounds like you want to round out your experience with functional programming. If you must do this the first time on a big project, that's challenging. But in that case, try to break your program into pieces that "maintain state" vs. "calculate things". The latter are where you can try to focus on "being more functional". Look for opportunities to write pure functions. Chain them together. Learn how to use higher-order functions. And finally, connect them to the rest of your application -- which can continue to be stateful and OOP and imperative. That's OK, for now, and maybe forever.