So what is American Hirschian Torah Im Derech Eretz? Well, it is fundamentally Hirschian Torah Im Derech Eretz. He is the foundation for a modern understanding of Torah Im Derech Eretz. However, 125 years have transpired since his passing and the world is vastly changed. It is important to note that we are still in the modern era so it has not changed as much as it did with regard to Torah observance between his era and the pre-modern. Yes, technology has exploded maybe even as much between our era and his and his and the prior, but philosophy, society, government - all that stuff puts us in a similar era to his.
So what's the American piece? For one, it has a different stance on Zionism. R' Hirsch generally was opposed and he referenced the three oaths from the Gemara in Shavuous. However, some significant events have happened since then: the conference at St. Remo, the UN Vote in '48, and the Holocaust. According to the Ohr Somayach, the vote at St. Remo alone nullified the three oaths. So all the more so for the other two events.
Besides that, half of Jewry lives in Israel today. Moreover, there really isn't much of a secular Zionist movement anymore. The threat of a Jewish identity outside of mitzvot, which was the real basis for opposition to Zionism, isn't that relevant.
You can argue that the Mizrachi movement has Hirschian qualities in its orientation of engagement with life. We are not Jews only in the beis midrash but in the field, in the army, in the lab, etc. The problem with Mizrachi was their involvement with the non-religious. Austritt is a big part of TIDE, but Austritt may have changed too. R' Hirsch's Austritt consisted of pulling away from a dominant reform community that was openly and actively opposed to mitzvah observance. Many worked with the government to shut it down. It operated in a city that had gone from a strong hold of Torah to a place with 100 frum families by the time R' Hirsch arrived.
Was the Washington Heights Austritt against Yeshiva University constructive? George Frankel argues that it was not or at least that it should not continue. The Hirschian community, he argues, needs to team up with YU, lest it be swalled by Haredism.
So the Austritt is different too. I think you can just as easily argue for an Austritt against the Haredi world as the Modern. Both take a different course than TIDE. However, I don't see the point of Austritt against Orthodox groups. We are up against 7 billion heathens for the most part. We need each other. The Haredim remind us of the need for resistance to the world and for a seriousness in life. The Modern remind us of the need for proper engagement with the world.
Thus, American TIDE is more complex and looks to more places. For example, I don't see how one cannot not look to the teachings of R' Joseph Soloveitchik. While he was a Torah u'maddah personality, much of his Torah spoke to TIDE. Same goes for R' Kook. Recall R' Hirsch's criticisms of the Rambam in the 18th letter of the 19 letters. R' Hirsch criticized the Rambam for being influenced by the Arab and Greek philosophy in his idealism of the the philosopher and his making mitzvos a handmaiden to it. I think this is an incredible and bold insight and it informs us of some of the flaws in the Haredi world today, which does something similar with Torah study. Nevertheless, R' Hirsch still called the Rambam a great man who saved Judaism. This idea of throwing people away for saying anything one does not like is a contemporary fad. So one can enjoy R' Kook while setting aside some of the more strident Zionism. Same with any of the great figures who don't fit in perfectly with contemporary agendas of different groups. Most of the time these people just talked Torah. You can study it. If they said or did something that doesn't align with Hirsch's TIDE (as you would expect him to apply it today) then just ignore that part. Would R' Hirsch approve of an Advanced Talmudic institute at Stern College? Hard to say. My guess is no. But that doesn't mean you can't study R' Soloveitchik who gave the opening shiur there.
American TIDE also would not be limited to 19th century high culture as I would guess it did in Frankfurt. Could it include Jazz music for example? Not sure. Maybe in limited quantities. Could it include folk music? These are all the questions we must ask.
I think this is one reason that Hashem gave us Rabbi Soloveitchik. Our era needed a gadol to present Torah that was not limited to Frankfurt Torah Im Derech Eretz. We needed someone who could talk about despair, even his own, who gave you more leeway in which to operate. That doesn't make him a Torah Im Derech personality in the Hirschian sense but maybe in the 20th century sense of it. R' Hirsch talked often about God as a loving God. The Rav even called God a friend. I believe that was needed for many in our era. This stuff isn't simple.
The main thing is to formulate a TIDE that works constructively for you, that inspires you to be your best. Today, it's highly personalized. You really have to work at it.
It's my view that contemporary Modern Orthodoxy is not Hirschian. Same goes for Haredism. The former is overly engaged with secular society. The latter hides not just from the world but oftentimes from life. This doesn't go well for people who work in an office 60 hours a week. It's hard to be motivated only by Torah study when you have only an hour a day for it.
Hirschianism is a wonderful alternative to these, containing elements of each. However, most people need to apply it to contemporary life - I call this application American Hirschian Torah Im Derech Eretz.