Hiddenveil
I am any transmigrator and directly at that time I choose to be the disciple of the uzumaki myth, especially if I am from the Uchiha clan or a genius that stands out, mainly because unlike Naruto who did not realize the political power that he had mainly because Sarutobi (although Naruto is also quite dumb and lazy when young) it doesn't seem right to him and he doesn't want an intelligent weapon no matter how much he says that Naruto is not a sacrificial weapon he did not give him the training or the knowledge that Mito transmitted to Kushina shortly before becoming Jinchuriki. But well the point is that Mito is a powerful political figure, she always was and even Danzo, Sarutobi and the clans make it clear that they did not dare to challenge her at any time, that is, you are her disciple and you directly receive "total protection" and "political independence".
a close uchiha with a jinchuriki let alone being her disciple, it's not going to cause public prejudice, think about it too. Even if Mito has a high political position she can't refuse the daimyo's orders, it's likely daimyo will tell her not to accept him as a disciple with excuse of endangering jinchuriki