In Imperator: Rome any Greek nation can send a competitor to the Ancient Olympics, even the far-flung Diadochi states. These Greek nations can even send a courtier who isn't ethnically Greek or an adherent of the Hellenic religion to compete.
So do we have records of non-Greeks, or people who didn't adhere to the Hellenic religion, competing in the Ancient Olympics? Also, did the far-flung Greek states like the Seleukid Empire, Ptolemaic Egypt, Massilia, the Bosporan Kingdom, Phasis or Menesthei regularly send competitors to the Ancient Olympics?
Prior to Roman Emperor Augustus, Olympic participants were limited to Greek freemen from any Greek city-state or kingdom. Non-Greeks and women were banned from participating. After the initial Roman conquest, the Olympics were largely ignored by the Romans, culminating in Sulla's pillage of Olympia and other Greek treasuries in 86 BCE.
After Agrippa restored the Temple of Zeus at Olympia, Augustus asked King Herod of Judea to finance the games. From Augustus on, Roman emperors had their busts enshrined as gods in the sacred grove of Zeus at Altis. Early on, Romans (including Tiberius) only participated in the equestrian events.
During Nero's reign, he ordered that all four of the Greek games (other three were Pythian, Nemean, and Isthmian Games) be combined into a single one that occurred in 65 CE in which he introduced music as events. He won the chariot events even though he was thrown from his carriage. He won the music events because the judges were too afraid to not award him the victory. After Nero's assassination, the so-called Neronian Olympiad was declared void.