Hippocrates nd Galen's ideas were around for so long because the church supported thier ideas and their ideas were reasonable.
Main way medieval churches helped medicine is setting up formal medical schools across Europe.
Main way medieval churches hindered medicine was rejecting ideas that challenged the bible or broader church ideas.
Medieval church helped medicine by offering alms in churches (offering more moeny to the poor) to pay for the sick.
Many churches had limited bed space to care for the sick. (Hindered medicine.)
Churches were used as hospitals for the sick and elderly. They would only care for them there.
The church made everyone pay a tithe (tax) to them which was used for religious reasons. (Hindered because some of that money could have been used help develop medicine.)
The church trained formal 'docters' ,however it was limited to only rich men. (Help because there are more trained people to cure and care for the sick but also hindered because they only trained men meaning less amount of potential docters.)
Majority of books were transcribed by monks, only church prescribed texts. (Hindered because the monks and curch can change the information in the books to make it ideal for them.)
The church outlawed human dissections which couldn't allow docters to study the right anatomy and instead use the inaccurte anatomy of pigs and monkeys.