I am getting an "Insufficient Privileges" error when I try to create a user with profile "Customer Community User",after going to "Enable Customer User" from "Manage External User" on the contact page.
I had this on a trial org's sandboxes. I was able to create community users against "Customer Community Plus" license type profiles, using "Enable Customer User" on the Contact, but I would get this "Insufficient Privileges" error when I tried the same against "Customer Community" license type profiles.
I contacted Salesforce who enabled both "High Volume Customer Portal" and "Lite Portal" licenses on the trial org (which I then matched down to the sandbox).
This resolved the problem for me but your mileage may vary.
BTW, to directly use the standard "Customer Community User" profile with a Digital Experience (community) you must now go to Setup > Digital Experiences > Settings and enable the Allow using standard external profiles for self-registration and user creation preference as covered here.