Well, here are my 2 cents:
Learn as much as possible. Never stop learning! But be sure which order is the right one for you. What do you need t the moment? For your current project? What technology is good in terms of things you already know.
As an example (looking at the libraries you ask about):
- Angular (either 1 or 2) is a bad idea. It mixes up everything web developer's agreed to separate (because it makes sense to separate). You will have to put your logic into your structure ultimately making overview hard for you and even harder for your team. Also you might sometimes not be able to mix, match and reuse partials because of Angular.
- Same for Ember. Really, those things were designed when we did not have HTML partials, yet.
- Backbone serves a completely different purpose: data locality. That's a good thing and you might want to learn it. You can combine it with a Flux framework of your choice in order to keep action in your JS and define bindings in one central place.
- React is one implementation of Flux. The idea is good, so I guess you should go for it in case you plan on making applications with web technologies.
- Vue... I have never played around with Vue, so I cannot tell you anything about it, sry.
Now you might wonder, what interface framework I think is a good idea. Let me redirect you to https://www.polymer-project.org/1.0/ . Polymer is like using templates with HTML, JS and CSS. Packed together to a unit. Directly in HTML (at least that's the vision).
tl;dr: Go for React, Polymer and Backbone. You can use all three in one project, so you do not really have to decide for one or the other with those.