Actually critical thinking in fact does come from a liberal philosophic tradition so on that charge, you are correct. The word liberal just as the word conservative has become abused as a result of 20th century politics and statism. Prior too, the word
liberal meant something else indeed and without "liberals" the ideal of the origins of America if not America itself would not even exist. Because the current ideal has so corrupted badly the word doesn't mean the word itself is valueless and thus in need of abandonment. I consider the ignorance of the user of the term, on both side of it, rather than the unworthiness of the word.
With all forms of engineering, critical thinking does indeed play a role. In my own world of engineering, in the case of a failure, I use root cause analysis which is a form of critical thinking in order to determine the root cause of a failure. Thus we arrive at a preventative measure and can even go so far to arrive at a possible predictive measure. Moving into predictive engineering makes me one of the few people at UPS whose true job is to discover a means to eliminate my own need. I once left a Corp. PE manager speechless who made the mistake of asking me what the purpose of my job was. His own fallacy of built in assumptions left him vulnerable to what I had to say. Never tell them what they want to hear that just re-enforces their assumptions!
I know someone who has 4 degrees including a degree in economics from Ga. Tech and he drives feeder and did so while earning those 4 degrees. Another feeder who has a degree in education and could be a teacher. I also know a Phd who runs and owns his own tree service because he loves the outdoors and trees. He's also a certified arborist who is helping me try and save my young Red Oak as we speak from a fungal attack.