Begin was the closest thing to a frum PM that Israel ever had. He was very pro-torah, and reached out to the gedolei yisroel. He also kept shabbos and Kashrus. From what I’ve read about him, I think he would have supported sefardim maintaining their religious traditions, why wouldn’t he?
Yabia, you’re focusing in on one rabbi that i mentioned. He wasn’t just meikil, he was capitulating to zionism. Ashkenazim had that too with shlomo goren. Sefardim had it, although he wasn’t as bad, with one of their chief rabbis. Rather than let his opinions fall into the obscurity they’re supposed to, eliezer melamed based his fake conversion standards on him.
Rav ovadia was a far greater figure than him anyway, and he was very meikil in general. Ashkenazim had their meikilim too, like the naharsham, for instance.
Name one p’sak from rav ovadia that was machmir like the ashkenazim – you won’t find it. What you will find, is kulos where he allows sefardim to eat in ashkenazi restaurants who rely on the rema for bishul akum – he bases it on being metztaref the yesh omrim in shu”a that beis yisroel is entirely mutar.