The discussion about modern orthodoxy is irrelevant to Yeshivat Har Etzion, located in the village of Alon Shvut in the Gush Etzion area, halfway from Yerushalayim to Hevron.
The Yeshiva is a hesder yeshiva for Israelis, with a contingent of Americans and other foreigners who come to learn for a year, two, or more. There are no secular studies, although there are many shiurim in non-talmudic areas of Torah. Again, the yeshiva is an Israeli yeshiva for Israelis, and not an American yeshiva plunked down in Israel.
While the roshei yeshiva have their own personal hashkafos, the learning is learning in the Litvish tradition, and it is top-notch, period. Therefore the discussion on whether Rav Lichtenstein Shlita, or any of the other three Roshei Yeshiva (not American)are MO is irrelevant.
Whoever studies there has chosen well. Hatzlachah.