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

During the post-Mauryan period, foreign invaders such as the Greeks (Indo-Greeks), Shakas, and Kushanas sought social and political integration into Indian society. However, they faced significant barriers within the orthodox Brahmanical system (Hinduism).

• Caste Barriers: Hinduism was characterized by a rigid varna (caste) system. These foreigners were often classified as mlecchas (barbarians) or relegated to the status of "Vratya Kshatriyas" (impure or fallen warriors), which denied them high social prestige.
• Egalitarianism: Buddhism was socially inclusive and did not recognize birth-based caste distinctions. This made it far more attractive to foreign elites who wanted to be part of the ruling class without being subjected to the social stigmas of the Hindu hierarchy.
• Institutional Support: The Buddhist Sangha provided a structured environment for cultural and education exchange, facilitating the assimilation of foreign rulers like Menander and Kanishka.