As I said, GitHub Pages are limited to public repositories in the free plan. If you go to Settings of your free private repository you'll see the following message in the GitHub Pages section: "Upgrade to GitHub Pro or make this repository public to enable Pages."
That's why GitLab does it better in this case.
Whoops, my bad. I saw the "free private repos" blog announcement and immediately tried it. Seemed to be working fine and private, but I forgot that I have acquired GH Pro recently. Yeah, GitLab is certainly still the way to go for private hosting.
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