There should be a check so that an error is shown when cookies are disabled. This will be added in an upcoming release.
Below you can find a workaround which checks if cookies are enabled, and only then loads mxui.js which bootstraps the Mendix client. If cookies are not enabled, an error is shown. The script should replace the inclusion of mxui.js in the document.
Sounds like it needs a bug report. I think there is a cookies-enabled check missing somewhere. If cookies are disabled, you should just get an error, since it would render the app completely useless since the app cannot track any state.