BuddyPress.org

RSS is probably disabled because the group is private.
If it was made available, anyone could access your private group’s activities!

Though if you’re logged in, it should work fine.

You could hack the groups_action_group_feed() function in /bp-groups.php to make this wide open though.
Or remove this function and create your own.

The problem is WordPress doesn’t support HTTP authentication, which is what is used for most password-protected RSS feeds.

Not much you can do at the moment… unless someone else has any other ideas?

Unless I’m wrong, that plugin requires users to be externally authenticated, so it doesn’t take into consideration WordPress’ existing accounts.

There is Private rss plugin that uses authentication https://wordpress.org/extend/plugins/private-rss/ (Not sure how it would work for groups)