I 100% agree that religion hindered the development of medicine in the Middle Ages.
A large part of many religions, specifically Christianity, often saw scientific advancements as going against God. This made it difficult for any medical developments to be made without the creators being accused of some form of religious treason. Many religious people believed that we should rely on God to solve problems— that sicknesses could be cursed from God in repayment for sins, and that the only way to repent was to pray / etc.... not to mention, many medical developments relied on ideas which the religions would reject. An example of scientific fact denied by the church is the fact that the earth revolves around the sun: the church strongly believed that god created the earth, and that everything in the universe centered around it, so the man who brought up this idea was strong hated by the church despite simply bringing up scientific fact.
Similarly many medical advancements were disliked by the church for being “too radical” AKA relying on new facts which seemingly “went against God” in some way. Furthermore many people simply didn’t even try to search for medical advancement as they believed that God would control it, that he was the cause, the question and the answer; that if you were sick it was because God made you sick, and that the only answer would be preexisting methods or praying, basically. The mixture of prosecution of people for science and the belief that God would fix everything greatly hindered the development of medicine in the Middle Ages.
Lastly, big religions arguably contributed towards the up keeping of societies without a middle class because of the great power given to the church in certain cases. This separation meant that most of the people who had access to any form of scientific or medical equipment were controlled by or directly involved in the church, with everyone else being too poor to even feed themselves, let alone pursue medical advancements; so then the church essentially controlled the medical advancement as a result of them controlling the more wealthy populations who had access to any possible advancements.