A standard state machine with no memory (other than the current state) is equivalent in expressivity to regexes (in fact regexes with back-references are more expressive); even if the state machine is non-deterministic.

The question is not about parsing. It is about tokenizing XHTML. So you are suggesting to write a hand-rolled tokenizer instead of using regexes for tokenization? Why is that better? That is exactly the kind of task regexes excel at.

A regex is a state machine. You can code the state machine by hand, but that does not invalidate the previous statement.

Depends on how you look at it.

Regex is a family of languages each of which can have various implementations. You could have a regex implementation that instead uses mutually recursive functions etc.

What is true is that regexes are typically not turing complete and can be represented with simple state machines.