I have to say that if I was in hospital as a patient and some nurse or doctor tried to 'pray for me' or talk to me of religion I would be more than upset, I would be tremendously angry. The worrying and frightening thing is, though, that if I was very ill and in much pain I might be reluctant to voice my dislike for fear of possible 'repercussions' in my medical care.
In my experience some people with a strong religious faith simply do not understand that their ministrations are not wanted and can come across as, and actually be, 'pushy' in their efforts to 'help' a poor ignorant person like me who doesn't want them to peddle their religion in my direction. It is equally true that I have known a few deeply-religious individuals who were exceedingly discreet in their faith, without in any way hiding it, but they would never dream of imposing their religious views on others who did not wish to hear it; I certainly respect such people and would never belittle their faith.
For the avoidance of any doubt or confusion it should be left to patients in hospital to express a wish for some kind of spiritual guidance or support - and to the chaplaincy service to provide it. Personally I have no objection to a nurse or doctor wearing a small and unobtrusive crucifix (for example), but unless a patient seeing it asks them for support of a spiritual kind they must not take it upon themselves to offer this - and if I was not actually in extremis and such a thing happened to me I would like to think I would have no hesitation in telling the person who had done so to 'get knotted'!