The makers of Grooveshark took the time to explain why the HTML 5 based website fails to work on the windows phone. They explain that due to a bug in the implementation of cross-domain AJAX requests, Internet Explorer (both on the desktop and on the phone) cannot make an AJAX call to an HTTPS endpoint from an HTTP page. They claim that there is an easy fix for this (serving the entire website using HTTPS), but “that is not possible right now”.
We would encourage the developers of Grooveshark not to give up, and go the last few miles. Build an HTTPS site, Grooveshark, that will solve both the wp7 issue and will generally be helpful with privacy concerns.