Dulwich Hamlets have become a very left-leaning support base, who seem to be inspired by St Pauli etc, and has now become rather self perpetuating.
Liverpool and Celtic may dine out on some things that some people could consider left-wing but I wouldn't write home about it. Both clubs massively exploit their fan bases and Celtics shtick has always been Irish republicanism, which is fawned upon by some leftist people but is independent of any real ideology of that sort. Liverpool do offer some Ł9 tickets to home fans but generally there is nothing really left-wing about either of them. They are big stinking greedy rip-off merchants.
My understanding has always been; St Pauli, Real Vallecano, Livorno (who wave USSR flags 😬) and Hapoel Tel Aviv as being famously left-wing fan bases. I believe the upwardly mobile Union Gilloise in Belgium are too, but often this is just twitter talk, a bit like how Swansea are best buds with Den Haag but 95% of Swans fans couldn't point to it on a map
I'm not sure of any genuinely left-wing football clubs though, and what would it even mean? I have far more respect for Brentford in changing their shirts every two seasons or the ticket prices charged by any German club over the hypocritical iconography used by the likes of Liverpool and Celtic