A google font set as the main content and headline font works in customizer, but doesn’t in live after publishing. The reason very simply is that “link href fonts.gstatic.com” is included in both versions, but the
“link rel=”stylesheet” href=”https://fonts.googleapis.com/css?family=…”
is not.
I’ve solved this for now by adding that line to my head manually, but this is of course not optimal.
There is also (maybe connected) a cross-domain referencing error for another font that is stored locally, because it is embedded from the main domain, not the staging subdomain in question.