The perception that the radio buttons are working on desktop browsers is optimistic!
In fact, they do not work correctly anywhere, because somebody wrote some extremely poorly-thought-out JS. Not knowing how to correctly use the Forms 2.0 JS API, they're overwriting the value attribute of the radio buttons after fetching a response from an outside webservice. Remove the code that calls updateFormVars and you'll be fine.
(Also, I shudder to imagine what you're doing with that service and its is_anon check, etc.. That's a clear Denial of Service attack vector if indeed it's hitting Marketo REST API with every pageview.)