Have the people proposing this never been exposed to the Constitution of Virginia or the Constitution of the United States? If elected officials don't include a religious exemption, then they are failing to uphold these Constitutions - which they swore to uphold when they took the oath of office - and are therefore literally guilty of treason.
Thr section of Virginia's Constitution known as The Statute for Religious Freedom was used as a model for the First Amendment to the United States Constitution. However, Virginia's Statute for Religious Freedom is not simply about separation of church and state - it also includes Freedom of Conscience. Mandating vaccination for those whose whose deeply held beliefs are contrary to taking this vaccine is in violation of both their civil rights and their Constitutional rights.