We are running exchange 2013/office365 in a hybrid environment.

On two security groups, I add a group to the allowed senders list and then get the following error when I hit save:

Members can't remove themselves from security groups.  Please reset the group to Closed for requests to leave.

I only see this error on two groups.  The other 200+ worked fine when changing them.  Any ideas?                          

You could use the cmdlet: 
Set-Distributiongroup identity <DistributionGroupName> MemberDepartRestriction Closed.

And for better understanding of that cmdlet works check this out:

https://technet.microsoft.com/en-us/library/bb124955(v=exchg.150).aspx

I ran that command and the error still happens.  I actually tried that before posting this thread.