Is it permissible not to make up two days of fasting that were broken by mistake, based on the اختلاف المذاهب الفقهية (differences in jurisprudential schools of thought), even though making them up seems to be the correct thing to do in one's inner self?

If you believe that the view asserting the obligation of making up [missed acts of worship] is the most correct, then it is incumbent upon you to make them up. An ordinary person is not given a choice between the opinions of the scholars as long as they believe one of them to be more preponderant.