I agree. Critical thinking is often paired with developing the methods or tools of critique. Instead of applying the tools of critique to one's own thoughts, these tools get applied selectively to ideas, especially ideas one doesn't agree with already.

For example, recognizing bias is a component of critical thinking. Rather than recognizing one's own biases, the reactionary thinker will instead tend to recognize bias in other's assumptions and arguments. They apply different standards to their own thoughts than they do to others'. You're absolutely right that this isn't critical thinking, but it is definitely a result of half-teaching or half-learning the tools of critique, or an inability to be intellectually honest or emotionally available to being wrong.