My personal problem is that people start to present themselves as "React" or "Angular" developers, which is kind of scary for me personally.

It is also hard to explain that you can pick up their framework (e.g. switch to Vue.js from React), many companies just say "no" unless you can provide strong experience. Some companies have better policies and they insist only on core knowledge and principles, but, unfortunately, I personally find them to be in a minority.