Allow access to specific plugin/page on member-only site

Hi, I have a website that is member-only, in that you must log in to view any part of it. I have a calendar plugin that allows members to subscribe to an .ics feed, which is located at https://website.domain/?plugin=all-in-one-event-calendar&controller=ai1ec_exporter_controller. Because the website is member-only, however, calendar applications can not get events from the feed as the access is blocked by wordpress’s authentication.

Is there a way to allow access to a specific plugin/page on a member-only site? Even a workaround would help.

If not, I’m thinking of writing a php script that takes input, grabs the data from the website using authentication, then outputs the feed back to the user. How can a page request be authenticated in an automated php script? Or is there a way to allow access to a certain IP address (localhost/127.0.0.1 specifically)?

Thanks