Legal Question in Business Law in Texas

Yes and yes.

Unless it is being done for a discriminatory reason against a protected class (race, creed, color, national origin, etc) or you are a govermental (civil service/teacher) worker or a Union worker. Texas has termination "at will" of non-contracted employees. If they don't like the shirt you are wearing, you can be fired for it. NOT that way in most States... but here, Yep!

So if they are doing this intentionally and non-dsicriminatorily, maybe they are trying to signal to you to move on! Can you transfer to another department? Are you always getting assigned the bad work and are they evaluating you badly for the work you are missing while being reassigned? IF so, maybe you should look at the big picture. Just a suggestion... Best of Luck!