While I'm not familiar with Django, I would assume that extending the Magento API to authenticate users would be possible, provided you're within the same domain or subdomain or have defined a cross-origin policy.
Some AJAX login extensions may provide this sort of functionality for you - here's one such extension:
http://www.magalter.com/fast-login-pro.html
There are a number of plugins available that provide single-sign-on with other platforms: Wordpress, SugarCRM, others. Perhaps looking into the source of those integrations would help you.
Some integrations:
http://jckemp.com/documentation/magento-wordpress-single-signon/
http://www.magentocommerce.com/magento-connect/wordpress-integration.html
A how-to series:
http://developer.blueearth.net/2011/11/16/magento-wordpress-integration-part-2/
Additionally, Magento's API provides the ability to fetch customers from the framework:
http://www.magentocommerce.com/api/rest/introduction.html#RESTAPIIntroduction-Customers
Lastly, consider using a single-sign-on solution with one of the major providers - OpenID, Google, Facebook, Twitter - all of which have Magento plugins available for user authentication. Then source something that provides this functionality in your Django app.