The caste system early in its creation was not as rigid a structure, based more on occupation than birth, however, it changed into a rigid system which defined rights and responsibilities at birth. This is not so say that personal history was not rewritten which occurred often during power transitions. Those who had taken power would rewrite their history to make their ancestors Kshatriya adn therefore have the right to rule by the caste system.

Now when it comes to the Greeks, they were outside the caste system and as such, the average Greek would be considered a mleccha, an individual who was an outsider to the caste system and did not conform to its norms. However this would not mean that powerful Greeks would be considered so tainting, they would be included in the caste system to fit within the world of the Indian kingdoms.

In a neat reversal of the usual classical perspective, they are a group on the geographical fringes of the civilized Indian world: the word mleccha, the outsider who does not subscribe to the norms of Indian society, is not simply strange, but barbarous.

For the most part, therefore, foreign groups whose political power demanded their social acceptance- or at least acknowledgment- had to be enrolled in a varna ‘by some legal fiction.'

This closed system led Greeks more to the Buddhists as they were more accepting of foreign individuals. This greater level of interaction is shown with the development of Greco-Buddhist art in which images of the Buddha became more hellenized, as shown by the use of the nimbus amoung other Greek artistic conventions.

Source:

The Hellenistic Far East: Archaeology, Language, and Identity in Greek Central Asia by Rachel Mairs

Apologies for going a bit off topic /u/a_wise_old_black_man. but could you recommend a/some book(s) on the indo-greek kingdoms?