You make some very interesting points but I will have to disagree with your comparison between the Covid-19 virus and mental illnesses.
It is true that we are not necessarily born with mental illnesses and that we can gain such mental illnesses from various external factors within our society, however, that does not give us the right to make the choice of a person believing in either science or religion to find the "cure" for their mental illness.
This issue from an ethical perspective is a very long argument which can be debated for hours on end.
On the other hand, it is our duty as humans to take care of mentally ill people at the best of our ability, whilst respecting their beliefs. I would say that say that we should interfere between their beliefs at the point where they might cause more harm than good for themselves. But, as mentioned before this is a very ethical issue which means that everyone can use a different theoretical framework to assume at taking the best ethical decision.