I’m now working with scripts in Airtable and am seeing the same error.
InconsistentPublicationsError: Site is published to multiple domains at different times
As long as the webflow.io staging and custom domain are in sync, everything is fine. As soon as they diverge too much, the error starts happening when sending updates using API calls.
To verify, after seeing an error, I went ahead and published both sites and re-ran my test. Was able to update without an error.