Yes, you can parse html with a state machine

As long as you have infinite states.
What? Turing machines can have infinite tape but my state machine can't have infinite states? Fuck you.

when people say 'state machine' they usually mean 'finite state machine', not Turing-complete constructions. it's a mental shortcut that can be unambigously inferred from context (just like how people sometimes use 'rectangle' to mean 'rectangle that isn't square') and you sound like an insufferable autist when you insert yourself into discussion to say that well ackshyually Turing machine is a state machine too