When adding groups to be allowed to access the self service website, the selection allows you to pick distribution groups along with security groups. But users who are added to the distribution lists are ignored and cannot access the self service website.
By design: Distribution Groups cannot be used when allowing users to access the self service website.
Enhancement Request 85709 has been submitted and will be considered in a future release of Password Manager.
Use security groups to allow users to access the self service website.
An enhancement request (#TF00626617) has been created to have distribution groups not appear in the selection when browsing groups in the domain.