If critical thinking is a universal method of improving human thinking it should help in different areas of human life. But in the same time it can not do that, because critical thinking can’t replace the whole amount of human knowledge with a number of skills, rules and dispositions. So it probably can help with thinking in scientific domains, for example, but not for X we are talking about.
How can we solve this paradox? Critical thinking can help people to choose better alternatives and follow this choice. And this alternative can be in different areas. Critical thinking can also help to check information about alternatives, which can help while looking for them.
So if a person needs to solve an issue in area related to X, he or she needs to gather some information about this area. Critical thinking can advice when one should stop looking for more. It is important factor because in many areas there are too many ways to solve simple problems. But these potential solutions can be filtered and partly evaluated during the search.
After this initial overview possible solutions can be compared with each other. Here critical thinking can help to choose the best source, later it can help to compare methods. In complicated cases critical thinking can point to scientific methods which can help to choose.
For example, a person may not have enough information in the moment and needs to try a solution before implementing it fully. Known scientific approaches can be used here to design an experiment and evaluate its results. It can be just a thought experiment or a computer simulation, but it can yield some useful conclusion.
In general, looking for alternatives and using an active open-minded thinking we can find solutions for one area in other areas of expertise. It is also a possibility to use tools and approaches from one area in another one. We can start looking for historical data how this approach was used in our area of interest and use critical thinking to find other areas we should check. After that we can find experts in this field or reliable sources to check, results of this search can also be evaluated with critical thinking.
As critical thinking helps people to work with information and knowledge, these tools can be used to find best solutions in different areas. Even complicated process of finding a solution can be broken down into smaller steps and critical thinking can be use on each steps to check how good is it. Another possible benefit of applying critical thinking tool on each step is a chance to find a very good alternative in the initial steps. In this case our common beliefs how it all works can be changed, but as a result the goal can be achieved faster or with less efforts.
I can only add that critical thinking also prepared people to change their beliefs when they conflicts with the reality. So this internal change wouldn’t be a surprise for a practitioner of critical thinking.