If you are getting the above error:
Check that your users have permission to create new records in your table, or in the linked table.
For example If your users permissions is set up so that 'the record -> company matches user, you need to switch on 'create record' in your 'Company' table for your users to save the record.
Check that the created by field has been set on that table.
Check that if the permissions relies on the M2M field on the user table and not on the record itself that this has been set correctly for the table that you want your users to save the record on.
If you are getting this error saving in admin as well as users, check that the field you have set in your create form is editable in your Airtable base.
If this field is locked and you have marked the field as required in your form, you will not be able to save the record.
Check that the Advanced settings in permissions is toggled off.
More information on using Advanced record creation permissions.