This is simply untrue! Josephus speaks of Israelites, beyond numbers, not subject to the Romans living in "Babylon" during the first century. You will find this in "Antiquities" Book XI, Chapter V, paragraph 2.
And when these Jews had understood what piety the king had towards God, and what kindness he had for Esdras, they were all greatly pleased; nay, many of them took their effects with them, and came to Babylon, as very desirous of going down to Jerusalem; but then the entire body of the people of Israel remained in that country; wherefore there are but two tribes in Asia and Europe subject to the Romans, while the ten tribes are beyond Euphrates till now, and are an immense multitude, and not to be estimated by numbers.
Matthew 10:5-6 directs Peter and the other Eleven to evangelize these "Lost Sheep" and not to go among the Gentiles. In 1 Peter 1:1-2 you will find Peter doing just that....evangelizing "Those with the foreknowledge of God". In fact Paul, the Apostle to the Gentiles....and Rome, was told to stay away from there [Acts 16:7].
You will find that Babylon was a little more than a caravan stop during the first century. You may not like the idea of Peter being there but both history and scripture verify it. They do not do the same for him being in Rome.....at any time.
You give the false impression that Peter was never to preach among the Genitiles.