Hmm, I’m not experiencing this.
I just installed and activated NextGEN Gallery, then went to the Customizer.
First, the Customizer wouldn’t load – it seems the plugin messes with the permalink settings. I went into “Settings > Permalinks” and clicked the save button to re-set my permalink options.
Then I went into the Customizer, and was able to choose my fonts without any issues.
Are you at least able to access the Customizer?