Why did people care so much about abstruse theological questions in the medieval period and why did it matter?

Part of what is involved in finding answers to this question is thinking through what is actually signified by the terms in the question.

The term "people" is very general. We don't actually know that every single person living in the Middle Ages was interested in abstruse theological questions. Given literacy rates of under 10 percent for males, we know very little about the thinking of most people as their thoughts have not been preserved....

Part of what is involved in finding answers to this question is thinking through what is actually signified by the terms in the question.

The term "people" is very general. We don't actually know that every single person living in the Middle Ages was interested in abstruse theological questions. Given literacy rates of under 10 percent for males, we know very little about the thinking of most people as their thoughts have not been preserved. Since literacy was to a great degree the purview of the Church and a few aristocrats and merchants taught in church schools, and monasteries were the main archives and scriptoria involved in recopying and preserving written texts, as we study the medieval period, the works most likely to be available to us are those which have some connection with the Church rather than a representative selection of the ideas of the general populace.

Next, if you are reading thinkers like St. Thomas Aquinas, Duns Scotus, or Albertus Magnus, they were professors of theology. Investigating abstruse theological issues was as much their job as investigating abstruse medical problems would be a doctor's job or abstruse mathematical problems a statistician's or mathematician's job. 

Additionally, there is the issue of what might be considered abstruse. All subjects are abstruse to you if you are not familiar with them. A theologian might find double-entry bookkeeping abstruse while an accountant perfectly comfortable in the world of ledgers and profits and losses might be puzzled by the significance of the filioque in the Nicene creed.

Finally, religious issues for Christians of the period were ultimately practical concerns. For people who believe literally in Christianity, the choices one makes in belief and worship, and in conforming one's life to religious principles, make the difference between eternal salvation and eternal damnation. This is something believers care about. Making bad decisions about practical matters of secular life might result in a few bad years, but for Christians making bad theological choices could result in billions of years of agony in the afterlife. These consequences made theology matter.