The Covid experimental shot, not a real vaccine, should not be put on the required vax list. It does not work and its effects are still not fully understood. 
Further, the required vaccines for K-12 and higher Ed should be dropped. The higher Ed requirement was enacted in 1984. I seriously doubt there has been any benefit to this regime. I estimate 20000 students enter higher Ed every year in Virginia and have to spend 2 hours or more on the medical forms, then you have to process the exemption requests. The paperwork and lost time I believe exceeds the benefit. Most parents choose to get most of the vaccines for their children. A waste of time. 
Finally, if you are to retain the mandates, you must strengthen the religious exemption, in accordance with the VA Constitution. UVA and other schools required essays explaining their faith and denied many requests. No. It is a right.