The problem with your logic, is that you are counvinced that the public releases are accessible on Patreon without registering as a patron, while they are not.
But they are... You don't need to be my patron to download a public game version either from the main post/about section, or any of the posts that I make for specific versions of the game. This is the entire point of public versions - everyone can download them and play.
On which step you have a problem with public versions?
You can add a screenshot to your post on Itch. Do you mean this message? It's an age verifier and you don't need to actually make an account to confirm it.
I've tested it out years ago, and it works from EU regions. Can't say for your region. I can only theorize that Patreon may have additional checks for some Middle East countries or something like that.