I agree that the moderator needs to be the responsible party to the utmost extent possible. Members also need to be responsible and leave any group t hey feel is not respectful. After enough people leave, the group may or may not get the message, but that should be on them too.
Let's meet in the middle.
SUGGESTION: Create a "Code of Conduct" message page for all groups, always visible can't be deactivated. It would be linked on the sidebar like any other feature. It would be auto populated with the default text as decided on by Groups.io management, so all groups are encouraged to begin with this standard. However, since one size never fits all, add the following functions.
1) Owners (and moderators if so designated) can edit this text. If they do so, a bright red message appears at the top of the message page saying, "This group's Code of Conduct varies from the Groups.io default. Please read it carefully." (or words to that effect).
2) The message by default is auto-emailed out to new members when they are added. Allowing disabling this feature would not be something I would recommend, but I suppose if you countered it's removal with a different auto-emailed message stating that "this group does not auto-send Code of Conduct info out, please see the CoC page here (link), or contact the group's owner for more info." (OWTTE) you could allow it. I think that would weaken it's impact past my comfort level though.
3) Owners (and mods if designated) have the ability to manually send the CoC to the group or to a select person (or list of persons) ideally right from the CoC screen.
4) Ability to autosend the CoC at regular intervals if the group wants to set that up.
This way, you encourage but don't tie down creativity, freedom of expression, etc., encourage responsible behavior, and also reduce the burden of enforcement. The last thing you want is to get embroiled in what constitutes a "knee-jerk reaction" on a system with a likes feature and easy "quick reply" features which encourage knee-jerk responses.
Let the TOS be the arbiter of the allowable content (your pervue of enforcement), and the Mods be the arbiters of etiquette via the CoC (their pervue), and the Members be thus empowered to act in a fully informed manner (our own inherent responsibility). Getting more complex than that would be a can o worms you may not want, or be able to keep up with.