By default, there are two tests that are run before creating a contact in CiviCRM. You only have to pass ONE of these two tests for the contact to be created.
1) Do they have a first name and a last name
OR
2) Do they have an email.
There is NOT a "back-end setting for civi where [you can] make first or last name optional" but if you have an email address for that contact, it will not be required.
One work around if you need to import contacts that don't have either an email or a first name and last name is to create a dummy email address like 'dummy@example.com' and add this to the data that you are going to import.