[The Gracchii branch of the Sempronius clan was plebeian. At this point in Republican Rome, plebes were fully integrated into the senate and magisterial orders, so there aren't any conflicts of law to be concerned about (in this particular case anyway).
That is an interesting fact about the Sempronius clan that I did not know. However, I find it hard to imagine that he could simply vie for the tribuneship, being the blood grandson of Scipio Africanus. Wouldn't that branch of his lineage be first and foremost on the minds of the plebeians?
I just did a little research on the gens Sempronia. Apparently there were two gentes Semproniae, one patrician, the other plebeian. Again, being that the Gracchi were descendants of Scipio Africanus, I find it hard to believe that they were members of the plebeian gens.