Is it permissible for a Sunni girl to marry a Sunni man without the consent of her Shiite parents?

All praise is due to Allah.

A woman is not to marry herself off; rather, her guardian must give her in marriage. Otherwise, her marriage contract would be invalid according to the majority of scholars.

If a woman's family prevents her from marrying a righteous man from among the Ahl al-Sunnah, due to their disbeliefs such as distorting the Quran and declaring the Companions to be disbelievers, then their guardianship over her is forfeited due to difference in religion and coercion (عضل).

Therefore, the woman can marry without their consent. Her case should be referred to a Sharia judge to marry her off, or a just Muslim man in her country can marry her off.

And Allah knows best.