http://neosalexandria.org/syncretism/greco-buddhism-a-brief-history/Both these Greek populations got cut off from the Greco-Bactrians by virtue of a deal between Seleuces I Nikator and Chandragupta Maurya where these cities were ceded to his rule.
So while the Greeks in Bactria retain a large chunk of their Hellenic culture, the Greeks in Alexandria of the Caucasus and Taxila whilst retaining a large chunk of their Hellenic culture also began to blend it with a lot of Indian culture.
Buddhism in the time of Chadragupta Maurya and Bindisura were rising religions and the Greeks in these two cities clearly embraced it as from very early on these two cities were notable Buddhist centres. It is often said that Buddhism only got Hellenized at a later period when it was probably Hellenized very early on. Without its earlier Hellenization it is unlikely it would have spread at the rate it did.
Buddhism at this time still saw the Buddha as a man and the religion as being more a philosophy. The Greeks naturally took to this. In the West there were the equivalents in the Stoics and the Epicureans and the Skeptics and Democriteans whose philosophies were already floating around even in Bactria. The Greeks were still able to worship the Gods of the Greeks but practiced Buddhism alongside this without any major contradiction.