An employer is entitled to issue lawful and reasonable directions to its employees and failure by an employee to comply is grounds for disciplinary action. Conversely, an employee is not required to follow unlawful or unreasonable instructions.
Mandating vaccination is, AFAIK, lawful.
So the question is: is it reasonable?
Reasonableness requires consideration of all the circumstances. On the one hand, there is a requirement for invasive medical intervention, albeit, a relatively minor one. On the other are the particular risk to the employee, other employees and the employer's operations if the employee contracts Covid-19 and other methods that could be used to manage that risk.
This may mean that the instruction might be reasonable for some employees (e.g. those working in the prison hospital) but not for others (e.g. administrative staff with no prisoner contact).