Google make opting out of their tracking as difficult and inconvenient as possible, after all, tracking users across the web is their main source of income and profitability.
You can get better tracking statistics (Google doesn't share all the data it gathers from your site with you) with free and open source analytics software, either self-hosted or as a service. The one that I have most experience with is http://piwik.org/ and they make it easy for visitors to your site to opt out of tracking (they simply check a box and it's done) and without preventing them from logging into your Moodle (Moodle's session cookies still work).
Like Moodle, they have official partners that'll provide Piwik as a service: http://piwik.org/hosting/ and there are other independent service providers, as well as being able to install and host it yourself.
Disclaimer: I have no affiliation to Piwik or anyone who works for them.