Unfortunately most Sefardim, whether Orthodox or not, still give truck to Ovadia Yosef and Shas solely to put one in he eye of the "Ashkenantozim" against whom they still love to continue harboring such a grudge, irrespective of whether Shas supports the folly of "Land for Peace": it goes that deep!
Remember that Sefardic Jewry spent 1000 years living among Arabs, unavoidably becoming Arabised, with persistent Arabic traits and thought patterns to this day, which has both pros and cons. In the 1940s Sefardim were known as "Mistaravim" ie "Arabised Jews".
Sefardim, like Arabs, love a powerful, charismatic leader with a simplistic nationalist message; which is why they flocked to R.Kahane.
But in the absence of a Kahane today, they instead flock to Shas, poor sad souls.