The question of whether Rav Hirsch was Modern Orthodox has been bandied about by many people. I think this is a very intriguing question, and I have various thoughts worthy of mention that can, perhaps, combine to answer the question.
What I really feel about this question, however, is that it’s generally mis-stated. Rav Hirsch was college-educated, embraced modernity, preached in the vernacular and wore clerical robes. I believe that it was clear to (nearly) all of his acquaintances that he was Modern Orthodox. It seems to me that the question people are really grappling with is whether today’s Modern Orthodoxy can claim Rav Hirsch as a founding figure.
That’s not a simple question to answer, but I think that framing the question more accurately is the first step toward answering it.
(This is not relevant to the question of R. Hirsch’s location on the Orthodox spectrum, but I want to point out that the claim on the 19th century “Rebbe card” that he was “Dr.” Samson Raphael Hirsch is inaccurate. He never graduated university, and certainly didn’t get a doctorate. Also, for whatever it’s worth, R. Hirsch assumed the Frankfurt rabbinate in 1851 and lived there for the rest of his life. He looks rather young here, so I’m assuming that this depiction of him is from some time in the 1850s.)