Error 405 when save with Ajax

Anyone else have this issue ?

It seems that a few other people are having similar issues, me included:
[Local] Cannot add new media - Support - Local Community (I’m experiencing the same)
Duplicator Pro 405 Not Allowed NGINX - #4 by Pierre - Support - Local Community

It seems that the root cause is nginx being quite fussy regarding POST requests and their origin - but this shouldn’t be an issue for dynamic requests from wordpress/php.

Even the rather horrible hack of redirecting 405 errors to 200 messages as suggested here:

is not working.

Even a suggestion to work around this issue would be appreciated.