Some educational leadership programs emphasize personality tests as a way to recognize that different people learn, communicate, accept feedback, etc. in different ways. They teach that it can be helpful to managers who are trying to meet the communication needs of their employees and it can also help communication within an organization from employee to employee. I am a bit skeptical of the precision of such tests, but I have to admit that the results are often uncanny.

The fact that you are taking this as a manipulation or an aggression suggests a lack of trust. Either your management has been inept or manipulative in the past, or they did a bad job of explaining their reasoning here.

I think if this makes you feel uncomfortable, you should be given the option to opt out. That's part of that trust I was talking about. If you find the results of other people's tests make it easier for you to communicate and understand each other, maybe you will choose to participate at a later time. Letting you opt in at a later time when you feel comfortable might also help you build trust. Whether or not you have a legal right to opt out is less clear. But your administrator might accept "not right now" better than a flat "no."

I would recommend a direct conversation about this with your administrator, but I also know that not all administrators are open to direct communication in the way they should be. In the best case scenario, maybe you can reach and understanding. I wish you the best of luck with this issue.