As of version 1.1.0, released today, RPS Include Content now offers support for private content. Display of content with a status of "private" is still governed by user capabilities (i.e. the user must be able to read content set to private) unless you override the restriction by forcing content of this type to display regardless of capability.
You can do this by enabling the setting on the plugin options page: Settings > Include Content > Show private included content without restriction. Optionally, you may specify this attribute on a case by case basis using the "private" attribute in the shortcode like so:
[rps-include post="###" private="true"]
Please reopen this topic if you need assistance with the implementation or any unexpected results.