Firefox by default can block the opening of popup or new tab. Normally you get a small line of text at the top of Firefox notifying you that it was blocked and usually giving you the option to allow.
If not, in settings -> privacy & security -> block pop-out window -> exceptions. You can allow the entire itch site.
In no-script, you can check the option to trust itch.io and itch.zone
PS: I have been testing web games created in Godot and so far I don't have any problems and I also use Firefox with no-script.