One of the big differences between being Mizrachi and being Modern Orthodox that has become blurred over time is the difference in the level of religious observance and the philosophy underpinning the two groups. For many, the Mizrachi are just MO's living in Israel but in truth, this is not correct.
However, this misunderstanding leads many to criticze when leading Mizrachi rabbonim make statements that sound Chareidi in nature. Such was the case recently when Rav Shlomo Aviner was asked a question about modest clothing in women and gave an answer which, to the outside world, sounded uncharacteristically strict.
However, in truth, his answer was completely within the pale of what is considered true Mizrachi. The movement, it must be remembered, was started because of the conviction certain leading rabbonim had that it is a religious imperative for Jews to return to and rebuild Eretz Yisrael, not as a reactionary movement seeking to modernize Jewish observance in response to outside pressure. The initial luminaries of the movement such as Rav Zvi Hirsch Kalischer, zt"l, Rav Avraham Yitzchak Kook, zt"l, and av Yitzchak Yaacov Reines, zt"l, were no less pious, observant or steeped in Torah scholarship than their anti-Zionist contemporaries. Thus to expect a standard of observance other than that of strict traditionalism based on halalchah from Mizrachi Jews is to completely misunderstand the movement and its beliefs.
Thus Rav Aviner's comments were not extreme when viewed from that perspective. The Mizrachi Jew is not less observant than his Chareidi colleague but channels his passion and energies into not just Torah study but those activities which build and protect the land of Israel.