[Someone]

> Having StringBuilder be a private field on the parser instance is not an issue either - it is simply reused.

It doesn’t matter for this API, but it is a code smell. It makes the class not reentrant.

Talking of the API, I would make it simpler to use and more idiomatic by making the entire public API

   static IEnumerable<List<String>> parse(StreamReader sr)

That call would store the parser state (currently just the StreamReader and that reused StringBuilder) in a private inner class. There would not be a constructor of the publicly visible class, removing that code smell.