The Greeks were not Monolithic and Chazal acted differently to different Greeks.
Alexander the Great (Who was a Macedonian, not a Greek) was welcomed by Chazal and Alexander is still considered a jewish name.
After Alexander died, his empire was split in 3 parts. The 2 main parts concerned jews were the Egyptian Greeks (The Ptolomies) and the Syrian Greek (The Selucides–(Antiochus in Hebrew)) . the border between the Ptolomies and the Selucidies was Judea. The Ptolmoies were generally hospitible to the jews and allowed them freedom. It was the Selucidies who were brutal and did not allow judaism to flourish. it was under the Ptlomoies that the Septugent was written.