Bull. Just pass a law that says public sector employees who are managers of other public sector employees shall not exploit their public sector employees. There is no need for a government union in any scenario.
There shouldn't be a difference. No employee should have a union that collectively bargains.
The reasons are entirely legitimate and obvious: because the employee is offered a wage, benefits, and policy that governs the employment before she or he decides to accept the job. The terms and conditions are explicit, written, read, understood, and signed by the employee and employer as agreeable before employment begins. If one employee/employer agree to x, y and z, and another employee and employer agree to a, b, and c, that's fine. They agreed to different things, so they get different things.
There is nothing relevant in this context to "protection." The sale of services is inherently contractual, and contracts have terms and conditions that are known in advance before signing on the dotted line agreeing to those terms and conditions.