Initially, I understand the Macedonians had a Greek culture (Art, Religion, etc) because they were Greek. But then the Romans dominated the Macedonian Empire and adopted their culture too, and that fusion would give birth to what is known as Greco Roman Culture. But why did the Romans adopt their culture at all?
Trying a short answer that would sum up what is said farther below:
It's because the Greeks were there, representing the most influential cultural area, because their culture did not seem foreign to the Romans, because it was intelligible to them, and seemed to provide superior answers to familiar problems. — Beside its cultural prestige, the Hellenistic world (the Greeks and peoples influenced by them) were representing a huge "gravitational" mass, as population numbers and as geographical area, one that couldn't be easily "dominated" or eliminated, and that couldn't be treated by the Romans as the Carthaginians had been.
I doubt that saying "Romans adopted Greek culture" makes much sense. Until the 20th century Greek and Latin languages were part of the main scholar curriculum all over Europe. But a non-Latin and non-Greek culture (the Christian one, or the "European", or the "modern" one) existed at the same time. Could they be separated? Romans had "their own" culture too, only that was related to the Greek. They didn't renounced their own language, political and religious traditions, but without ANY Greek influence there wouldn't have been much "Roman culture" to start with.
This is like asking why Americans have "adopted" European culture. Greeks and Etruscans were a decisive influence even before Rome developed as a local power. Etruscans, themselves heavily influenced by the Greeks, have influenced the Romans to a such degree that it is very difficult to find original elements of Roman religion or politics that lack the mark of an Etruscan model.
Greeks had put their mark all over Italy long before Romans went out of Latium. They were present in the south of the peninsula and in Sicily, as well as in Marseilles. Rome appeared in an area at the periphery of the Hellenistic world, but one that was already under the gravitational pull of that world. — When Romans expanded throughout Italy and before conquering the Greeks themselves they conquered peoples that were themselves influenced by the Greek model. Farther expatiation to the east brought them fully into the Greek-speaking Hellenistic world.
Unlike Carthaginians and Persians, for example, Romans were in a way molded from their cradle into the Greek framework. This fact is reflected in the re-elaboration of the founding myth of Rome by Virgil, that presents the Romans as descendants of Aeneas of Troy, that is in opposition to the Greek, but also within the Greek cultural mold of the Iliad.
There were some moments of resistance to Greek influence, for example against the cult of Dionysus and against Greek philosophers, and Latin poets and writers had a clear conscience of the need to create a Latin literary tradition instead of just translating the Greeks. But the Greek culture remained present as a model, one that was clearly conceived as such by the Romans.
We must not forget that the idea of originality as a great value is recent, and was by no means present in antiquity. On the contrary, the idea of tradition was valued, it was even by definition what had value.
We could ask ourselves how come Romans kept a high degree of originality anyway (the way we can investigate the degree of originality of American culture in relation to Europe) in spite of the Greek influence, and in fact through that influence.
It is maybe because before conquering the Greek world they had already "adapted" to the Greek influences and to the Hellenistic world by assimilating fully into their own frame of mind and cultural forms sufficient elements of that great culture (like a sort of "antibodies") which allowed them to be able to translate the Hellenism into "Latinitas", instead of melting away into the Hellenistic ocean and be assimilated almost completely, like subsequently the Mongols were into India and China — or some Germanic peoples were into the late-Roman world, or the Turkic Bulgars into the Balkan world, a world that ended up Slavic-speaking, but which perpetuated the late-Roman model (misleadingly called "Byzantine" as if less Roman).
This question was already addressed on this site. Romans adopted Greek culture because it was higher than the Roman one. And this is not unique such case in history. For example Mongols (and other peoples) who conquered China adopted Chinese culture. Barbarians who conquered the Roman empire also adopted Roman culture.
On the statement that Macedonians were Greek, there was some disagreement in antiquity. They wanted very much to present themselves as Greek, indeed. For the same reason which is stated in the first paragraph. But not all Greeks agreed with this. (One of the Macedon kings, Alexander I wad a nickname Philhellene which seems to indicate that Macedonians were not considered Hellenes).