We want to allow members to choose and join groups on their own, how can we restrict group admin & moderators to add users in their groups?

Hi there, 

This is not recommended, but using a CSS code you can hide the "Add members to group" section from the right menu of the group. Therefore, no one will be able to add a user to the group:

div.ui.segment.group-add-members{
display: none !important;
}

Then you need to also hide the "Remove User From Groups" section via CSS code as well:

div.ui.top13.left.pointing.dropdown.right.floated.member-group-menu{
display: none !important;
}