It worked fine until a couple of days ago. I updated the Total theme, but since the error persits with other themes, I guess this should not have caused the problem.
I thought that maybe it was caused by a setting in the WP Super Cache plugin that disables users from changing certain .php files. But I changed that setting back and the error is still there.
Where can I make sure that my user has sufficient capabilities for the customizer? Where can these be changed?