How to Solve a Wonderful Mystery
The first issue we must recognize is the way God uses the word Gentile in His Word. The context will usually show you how the words are meant to be used. In addition, the scope of the particular section of a book must be accounted for. Before and after Acts 28:28 there are Gentile believers spoken of in the Bible some are called a wild olive branch while others are called The Church which is His Body, Why?
The Apostle Paul's epistles usually use the word Gentile meaning the Gentile believers in the many synagogues. The usage of Gentiles in Romans is especially of interest. Failing to discern this usage in Romans has caused much dismay over many years. It was the Gentile believers, who attended the synagogues, which were grafted into the olive tree, the olive tree being Israel. These were the Gentiles Paul spoke to in his Acts ministry with possibly 3 exceptions.
Taking a look at the scope of Acts, we see that the ministry to the Gentiles was for the benefit of Israel; God was not at that particular time interested in saving the Gentiles. God told Israel, in Romans 10:19,