Since I follow Rabbi Ovadia Yosef's Halachic rulings, which Rabbi should I follow in terms of Hashkafa: Rabbi Ovadia Yosef or Rabbi Mordechai Eliyahu? I heard that Rav Ovadia made a visit to one of the Shtachim. Does this mean he has changed his views regarding living in Yehuda and the Shomron?
Rav Ovadia Shlita has visited Jewish settlements in Yesha in the past. He - like all of the Poskim is "in favor" of Jewish sovereignty throughout Eretz Yisrael. He disagreed with many Poskim in that a decade ago he felt that concessions to the Arabs were required to save Jewish lives. The other Poskim's position is that Jewish sovereignty in the Land of Israel justifies going to war to defend that sovereignty. The more than 600 Jewish casualties in the latest intifada- known by many as "The Oslo War"- have proved to the vast majority of Israelis that concessions do not bring peace but rather the opposite. It is, therefore, not surprising that today the political supporters of Rav Ovadia advocate a hard-line approach in defeating the Palestinian Arab enemy. In answer to the theoretical side of your question, without relating to the personalities involved, one chooses a Rav regarding "Hashkafa"= Emunah on the basis of proven greatness in Emunah- a greatness based on knowledge, depth, and a willingness for personal self-sacrifice in pursuit of the ideals of Jewish belief. If you are writing from outside Israel, it is important to be aware of the fact that both Rav Ovadia Yosef Shlita and Rav Mordechai Eliahu Shlita stress the importance of living in the Land of Israel in fulfillment of the commandment to conquer and settle the Land.