Thanks to the wordpress forums, some grateful one just helped me finding the answer. So If you come here looking for a solution. Please first try the options I put in the post before, they did not work for me but they did for other users, so give them a try first.
If for some reason, just like me, you still have problems with the Customizer then open your console in google chrome and check for errors in javascript because as Joy suggested it to me here the Customizer has a lot of JS and specially uses jQuery.
To summarize, I could fix the problem by removing my calling to jQuery for Bootstrap in my theme and let it just use the default one in wordpress. So far, there has been no problem with the CSS library so I hope this is done.