In addition to having to follow the standard process to enable web application's anonymous access:
I had to do a few PowerShell commands to make anonymous access perform most activities on SharePoint without limitation.
1) Modify the root webs anonymous permission mask (you can reduce the access here too)
web.AnonymousPermMask64 = "FullMask"
2) Allow client calls for anonymous users
$webApp = Get-SPWebApplication http://forms.turnkey.global
3) I also had to enable iframes for other sites to point to my SharePoint forms