Many of the Greeks, Kushanas and Shakas embraced Buddhism rather than Hinduism because

Foreign rulers like the Indo-Greeks, Śhakas and Kuṣhāṇas found Buddhism institutionally and socially more accessible than Vedic/Hindu structures. Buddhist monasteries and sanghas offered non-caste communal spaces, education and cultural exchange that facilitated integration of foreign elites and artisans into Indian society [2]. Kuṣhāṇa emperors patronized the building of stupas and monasteries, making Buddhism a visible, institutional route to legitimation and local influence. The Indo-Greek king Menander (Milinda) is a noted example of Hellenic engagement with Buddhism, showing personal as well as political accommodation with Buddhist traditions [2]. The regional presence and syncretic tendencies of these rulers in north-west India also correlate with the rise of Buddhist patronage under Śhaka and Kuṣhāṇa domains [1].

Sources

1. [2] https://digitalcommons.ursinus.edu/context/history_hon/article/1001/viewcontent/auto_convert.pdf
2. [3] https://ebooks.inflibnet.ac.in/icp01/chapter/indo-greeks-sakas-and-kushanas/
3. [1] Exploring Society:India and Beyond ,Social Science-Class VII . NCERT(Revised ed 2025) > Chapter 6: The Age of Reorganisation > LET'S EXPLORE > p. 135