Hospitals in Denmark cater patients with their choices of food. Patients have right to deselect food that they do not like.
Patients can freely choose Islamic halal food. They also can choose vegetarian food. It is not just the hospitals, in every public institution people have to choose their diet. In schools and Kindergartens, parents can give instructions what kind of food their children eat.
There was debate some years ago, about halal meat when one of the largest hospitals in Denmark, Hvidovre Hospital chose to serve only halal meat to the patients. They argued, non-muslims did not have problem with halal food. Doctors did not find any hygienic problem in halal meat. They also got it cheaper. Here is the link of the halal meat story: Sandheden bag Hvidovre Hospitals halalkød
Some experts argued, that catering only halal meat was contradictory to Danish values. One of the fundamental values of Denmark that public system must not be influenced by the religion. The public system must treat citizens equally without consideration to religion.
If hospitals served only halal food, that meant system was influenced by the religion and special the privilege was given to a certain religion.
In general, patients have free choice of food in hospitals