I found the cause of the problem (with the help of the server admin).
You won’t believe it.
It’s WordFence firewall, operating OUTSIDE of the WordPress boundaries, in a subdomain. This F*cker was sneakily blocking “unsafe” post requests, without warning me.
After whitelisting these so called “unsafe” actions, Mautic went back to working normally.
So IF you have WordPress + WordFence on www.domain.com and you run Mautic on a subdomain, i.e. mautic.domain.com, then no matter what… CHECK WordFence if you’re running into Mautic trouble.
Even if your Mautic runs on a completely separated subdomain.
Weird but true…