[Michael Goldfinger]

To be more clear it is at the moment not possible to use google fonts with the exception of hosting them locally.
So either disable google fonts in general and only use other fonts like fonts.com, adobe fonts, font awesome, or host all needed fonts locally.

It would also be more convenient on the Theme->Customization->Typographic section to show the origin of the font like “Open Sans (Google Font)” and so on.
An option to download all used fonts automatically and use the local version would be perfect.

I tried using a plugin “Local Google Fonts” but it does not catch all fonts on your theme.

Also adding this option for other used font hosting services would be beneficial for the future if similar things happens with other font services too.