I know it is possible to create users with read-only rights to the monit page, but is it possible to create a publicly viewed status page with read-only permissions?
Afraid you can't:
If the Monit command line interface is being used, at least one cleartext password is necessary (see bellow), otherwise the Monit command line interface will not be able to connect to the Monit web interface.
https://www.mmonit.com/monit/documentation/monit.html#Authentication
Regards