If that's the case though, then why did it suddenly start happening? I'd played the game for a good two or three months before the issue cropped up and hadn't changed anything on my end regarding privacy settings.
Sometimes when an update happens the url et cetera that itch is hosting from for the game (which is running in an iframe) changes, People have definitely had that trigger the privacy stuff before when it wasn't.
Unfortunately there just isn't a fix outside of trying different browser or getting the proper whitelist setup et cetera.