How is it clear that religious thought and philosophy were totally intertwined during the Middle Ages? Why was it this way?

Interesting question. Many of the seminal figures in medieval philosophy (from Augustine to Anselm to Aquinas) were members of the Christian church. The earliest universities where philosophy was practiced were centers of theological practices (the art of disputation, for example) and were also sites where persons trained for the priesthood. Actually, in pre-Christian philosophy, many of the philosophers engaged in work that touched on matters that we would today describe as religiously significant (the existence of God or gods, the soul, an afterlife, etc). So, in a sense, in over 2,400 years of philosophy in the west, a majority of that time involved philosophers engaging in themes of religious significance. Even philosophers one might read in a secular light such as Hume and Kant spent enormous time and energy in the philosophical assessment of religious beliefs and practices.