Thanks for the replies to Jose and Joy. @jcastaneda No, I neither have any plugin active nor installed. I removed the ones that come by default with the fresh wordpress zip file.
@joyously , thanks for the suggestion, I tried after you posted it but unfortunately the Customize has not changed. I checked the inspector element in google chrome and the new div
wraps the widget like it is supposed to do, so nothing odd about it and the class in it is widget_text
since is a Widget Text as I mentioned on the main question.