There is a way to list specific non-members who are allowed to post to a Mailman list of which they are not a member. You must be able to enter the moderator controls to add people to the accept_these_nonmembers option list.
Add an address that does not need moderation when sending a message to a list of which they're not a member with the following steps:
1. Enter the moderator controls
2. Navigate to Privacy Options » [Sender filters].
3. About halfway down the page are the Non-member filters. The first option is the option for the List of non-member addresses whose postings should be automatically accepted. In the box to the right, enter the addresses, one per line.
4. Proceed to the Submit Your Changes button at the very bottom of the page and click it to save your changes.
Note: advanced options instructions are available by clicking on the Details for accept_these_members link.