Both religions taught that each person should take care of the sick and build hospitals. This encouraged people to help others and saw the general people learning more about medicine to try to heal people so helped medicine.
The Islam's adopted Hippocrates way of observation and were able to find out more things just the way that Hippocrates did himself. They learnt this from translated scripts. They also used chemistry in medicine and they discovered such things as distillation and sublimation, which in improving public health and less people got sick and therefore helped the development of medicine.
Christians used charms for good luck and believed in herbs in the same way the Islam faith did. The Islam’s developed herbal drugs such as laudanum, senna, musk, benzoin and Camphor. Both religions were able to do this because of the churches influence in opening universities and libraries with many medical books where people could study. This was the first in Christianity had people been able to start studying medicine since the fall of the Roman Empire. The Islam’s even had to have certain qualifications before they could become doctors so that they new what they were doing. Religion was able to help the development of medicine.
The Christian church did not have a total ban on human dissection but it was limited. But this did mean that people studying medicine in the church backed universities were able to study the human anatomy in a more detailed way than Galen and where religion had stopped Galen from the dissection religion was now able to help the development. Although the Islam's were not allowed to dissect they were able to study more of the anatomy by performing surgeries such as caesarean. In this case religion did not hinder the development of medicine.
The city of Baghdad made a good centre of the Muslim area because it had good access from rivers and land so trade was good. It made the passing on of information easy and the translated ides went further and further.
However much religion helped the development of medicine it also hindered the development.
Christians and Islam's were both unable to question Galen’s work. For one reason the Christians were strong believers that someone who believes in the one God in perfect and they did not believe other theories until much later on. The Islam's were unable to perform dissections due to religion, which couldn’t enhance anatomy study, and the Islam’s could find proof to prove Galen wrong. They also believed in the one God like the Christians and Galen. Here religion was no help to the development of medicine.
Up until 1200AD, the Christian church had very little to do with the development and certainly did not push it forward. Until then there was very little education and doctors to treat the sick. This shows that Religion hindered the development of Medicine.
So as you can see there are many factors of religion that both helped and hindered the development of medicine. I think that the statement is correct in that Religion was a hindrance to the development of medicine during the Middle Ages but it is wrong in that Religion also helped the developments.