I like to see all file extensions, so obviously this isn't an issue for me. However, in the interest of trying to find an answer for you, I've been experimenting with the setting. Strangely, I noticed that even when I UNchecked the "Show all filename extensions" option, none of my file extensions disappeared. Then I discovered that individual file settings override that global setting, and for some reason, apparently every file on my computer does NOT have "Hide extension" checked when I "get info" for the file.
I also discovered that when you're going to save a file in an app, on the Save As dialogue, if you click the view options dropdown menu, there is an option to "Hide extension" for the saved file. The app remembers this option the next time you go to save a new file.
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However, I don't see this option in Safari's Save-as dialogue. I DID see it in MS Office apps and got it to work. I did see it in Chrome as well, but for some reason it doesn't work there. It seems to work when you check "Hide Extension" because the filename immediately loses its extension in the field where the editable filename appears, however the saved file in Finder shows the extension. So it seems really inconsistent/buggy. IMO, the global setting (under Finder > Preferences > Advanced) should override EVERYTHING, but it doesn't for some odd reason.