Cron job url needs exception in multi site privacy plugin

I’ve a multi site setup and am using multi site privacy plugin and mailpoet email newsletter plugin. The plugin doesn’t work when privacy is on.

The plugin contacts an external server to run the cron job, with privacy on, this doesn’t happen.

Mailpoet support team asked me this :

is enabled on the site/blog.

A filter extensive testing there isn’t a workaround that’s currently available without modifying core plugin code, is there any way that you could perhaps use a different way of securing the blog that allows the cron URL itself to be whitelisted?