I have been using a DOMParser object to parse a text string to an XML tree. However it is not available in the context of a Web Worker (and neither is, of course, document.E
according to the spec
The DOM APIs (Node objects, Document objects, etc) are not available to workers in this version of this specification.
I guess thats why DOMParser is not availlable, but I don't really understand why that decision was made. (fetching and processing an XML document in a WebWorker does not seems unreasonnable)
but you can import other tools available: a "Cross Platform XML Parsing in JavaScript"
At this point I like to share my parser: https://github.com/tobiasnickel/tXml
with its tXml() method you can parse a string into an object and it takes only 0.5kb minified + gzipped