Last week the Jewish Press posted an article by Harry Maryles called: Merging the Orthodox Streams. In that article, Harry Maryles attempts to suggest that we bring a “broad Hashkafic spectrum under one roof.” While this sounds like an ideal, I don’t see that ever happening, unfortunately.
The truth is, until situations change, everyone is “on the same page.” For example, Avraham Avinu had in his household Yitzchak a forefather of Am Yisrael, Yishmael, the forefather of Arabs/Muslims, and Lot, the grandfather of the nation of Moav.
Once time passes people and groups branch off in different directions based on their beliefs. It’s completely natural.
That said, YU and BMG shared common beliefs when a) times were simpler, b) Many Jews had to go to work or starve to death, and c) just being Shomer Shabbos was a miracle. Today, none of that applies so the situation has changed. Now both Yeshivos focus on different strains. YU still emphasizes too much on Madda and less on Torah, and BMG sees the “frummization” of American Jewish society as an opportunity to “amp up” the learning.
Just my thoughts.