For Firefox there are a couple of other solutions for this problem, but for Chrome I have not been able to find any.
Note: The warning is there for security reasons, because sites can otherwise - via JavaScript - automatically fullscreen themselves, and for instance disguise themselves as your desktop, while intercepting user input.
This is particularly an issue as these solutions also disable the first, related popup that asks you whether you want to allow or deny the website to put you in fullscreen, not just the notification shown after allowing a site to go into fullscreen.
Firefox
1: Via about:config
- Type in
about:config
into the navigation bar and press enter.
- Search for the value
full-screen-api.approval-required
and set it to false.
2: Via a plugin
Install the Firefox plugin Disable HTML Fullscreen Alert.