Come on.
MO, while resembling traditional Orthodoxy in many ways, is not compatible with traditional Orthodoxy (though TIDE is compatible).
MO, including Rabbi Herschel Schachter as per his shiurim, believes in Zionism as a religious part of their religion. As in, for example, they believe it’s potentially worth sacrificing Jewish lives for the State of Israel (not just to help people there). That’s a huge break from, and wholly incompatible with, traditional Orthodoxy.
As well, MO holds that Torah and, lihavdil, Maddah both have intrinsic value. This is also not traditional Orthodoxy. It’s just Torah that has intrinsic values, even if we also study secular subjects for permitted (e.g. practical) reasons.
Not to mention the mixing of the genders and teaching gemara to girls, et al. which are all incompatible with traditional Orthodoxy.