How do we solve the problem about bad behavior (unfair evaluation) in lab?
From what you have written, it appears that the fundamental problem is that you are dealing with a nakedly corrupt organization. You describe your student as having been failed for blatantly political reasons that have nothing to do with their education. 

Such an action is obviously unethical, and should not be tolerated. The key questions that I see, then, are these:


Is there is anybody who you can work with in order to effectively oppose this corruption?
Does your student want to be a test case against corruption?


You describe your chair as being in favor of the current regime. You may wish to discuss in any case, as even if your chair doesn't like students who don't join the union, they may still be opposed to naked abuse of power by union members. If the chair will not act, are there deans or such who might? Are there other faculty members or student organizations who feel the same way as you? What about outside groups that might bring pressure, such as local or international media?

This does sound like an important fight to fight, but also remember that it is not only your fight. If their power is strong and you directly oppose them, the student union may choose to make life very difficult for your student, so before taking any direct action in opposition, it would be important to discuss potential consequences with your student. Since they did not simply take the expedient path and join the union, they may well be willing to fight; equally, however, they may have circumstances that make it problematic for them to do so, and it is not your right to make that choice on their behalf.