All secure RSS feeds now transparently support BASIC Authentication.
The behavior is such that when you're logged in, the feeds will simply work as expected if you open them directly in the browser. If you log out, you'll suddenly be promted for BASIC Authentication. If you use the url with an external RSS client and that client supports BASIC Authentication then simply give your credentials and you should be good to go.
Pleae note that BASIC Authentication transfers your passwords over the internet/network in plain text, so make sure that you have SSL enabled if you care about such things.
An alternative is also to enabled DIGEST Authentication (just add an init parameter for "digest_auth" in the filter declaration and restart).
Note of you're using an SSO of some kind, and the client making the request speaks in your SSO's toung, then of course you don't have to worry about any of this.
(Update: The issue was resolved as of LPS-12308 r73243.)