No, it should not be made compulsory, but I think it is quite acceptable to make it compulsory for some roles, such as those in contact with those in medical or social care.
Quite a lot of careers have physical and other qualifications that have to be met before you can enter them. Both DH and DS at one point or another considered careers in the armed services, but discovered that their eye sight did not meet the required standards. I consider that making the requirement that someone has to have the COVID vaccine, or any other appropriate vaccine before working with vulnerable people, is no different.