This is a simple preventive health issue. Vaccines help prevent the spread of illnesses. Some people are against them for religious purposes or they simply feel that vaccines don't work. However, it is proven that vaccines do prevent certain illnesses. If you attend a public institution funded by tax dollars, it should be required for students to be vaccinated.
Yes, students should be required to have vaccinations before entering school. Parents who put their own families and the families of other students at risk by not vaccinating their children should not have their conspiratorial ideas indulged by schools. For the good of public health, all students should be vaccinated.
With vaccinations there can be a tragedy of the commons. It's best if everyone gets the vaccination except for you. On the other hand, politicians need to make sure that everyone can get vaccinated, because that is the only way to truly get rid of disease. They need to enforce what is good for everyone.
Yes, students should have at least the minimum number of vaccinations before entering school. A college campus is a crowded place. In the dorms especially, diseases can spread very easily. It would be in everyone's best interest to be vaccinated against the basics: measles, mumps, tetanus, chicken pox, and maybe one or two more diseases.
There are some students, for example those with illnesses such as cancer or HIV/AIDS that are immunocompromised and unable to have vaccines. Should be disallow all of these students from attending universities? And while yes they do prevent diseases, (not the flu vaccine but most) they should not be required for entry into a university. I have not had my last meningococcal booster or my flu shot and I am currently sitting in a university dorm writing this as we speak. I have not infected or killed anyone, nor will I ever most likely. Its a personal choice whether to take preventative measures to protect yourself, what isn't a choice is whether to treat the symptoms once they strike. It is akin to not having insurance on your car, which I do not think the government should mandate. If someone wants to be an idiot you should let them, as long as they are not hurting anyone else which I do not believe they are.