A static cached page is just plain old HTML, it doesn't pass through EE or PHP at all. You cannot therefore escape regions of the page from caching:
Freeform forms cannot be cached as they require a token to be generated for each user that views the form, and that is only ...
The developer gave a solution here: https://devot-ee.com/add-ons/support/mustash/viewthread/15161
Change the following code on line line 664 in mcp.mustash.php:
'group_id' => $group[$index],
'group_id' => ($group[$index] == "NULL" ? NULL : $group[$index]),