What is the ruling on a girl refusing a suitor from the deviant sect of her parents, and what is the ruling on her marrying, against their will, a man from Ahl al-Sunnah wal-Jama'ah, given their aversion to this group and the difficulty of their approval?

There is no blame upon you for rejecting a suitor you do not desire, even if he is pleasing in his religiosity and character. How much more so if the suitor is not pleasing in his religiosity? It is preferable to avoid marriage with people of non-disbelieving innovations, and it is not permissible to marry someone who holds disbelieving innovations. Your parents do not have the right to force you to marry someone you dislike, for they cannot compel an adult, sane woman to marry someone she does not want. If someone whose religiosity and character you approve of proposes to you, and your parents prevent you from marrying him, you may take the matter to a Shariah judge to marry you or order your guardian to marry you.