I agree with this one, However there are two ways one could divide the central asian invasions, pre and post Islamic
Before central asians such as Indo Parthians or Kushans who invaded were buddhists as such became the patrons of Indian culture and saw themselves as Indians and Used Indian customs, traditions, culture and languages and allowed them selves to blend in
After Islam, The Turks who invaded all had a separate civil, legal, political, religious and cultural institutions, They all worshipped a foreign religion, spoke a foreign language and had persian based court culture, this can be said as the first divisions of society between Muslims and Non muslims, the end of this culminated in the creation of Pakistan
Well, the Kushans are a diverse group. Kanishka I was a Buddhist and in the Greco-Indian tradition of Buddhism. He however, was the only explicitly Buddhist Kushan monarch. All of the Buddha coinages derive from his reign. He however, is a patron not only of Buddhism, but of the Greco-Bactrian polytheist traditions. As I have mentioned elsewhere, the majority of the Kushan deities represented on coinage and devoted to are of these types:
1. Presumably Tocharian deities. The most famous is the Kushan royal tutelary deity, Winshu, a wind god often combined in Kushan inscription with Hermes and Hercules. This god, is postulated to be the personal god of the Kushan royal clan.
2. Greek/Hellenic deities: These are the obvious Greek gods. Most commonly of these depicted, is Zeus (also combined to Indra) and Apollo-Helios.
3. Iranic polytheist deities: This was primarily Mithra, written in Greek as Mitro on Kushan coinage. Anahita was also common as a goddess of the lake, rivers and the sea. Ahura Mazda appeared on, if if I recall, five or six coins, making it representative of less than 1% of coinages in discovered Kushan caches.
4. Hindu deities: The deities of the Subcontinent. This was in Kushan coinage primarily two deities of great importance. Namely, Shiva and Vishnu. The Kushan monarch Vasudeva I claimed to be a devotee of Shiva in his inscriptions. Subsequent Kushan monarchs, would focus upon Vishnu and the representation of other deities declined, within the Indus Valley or the Kushan southern kingdom or realm.
5. Buddhism: This is the depiction of Buddha in coinage or inscriptions, very rare outside of the reign of Kanishka I.
6. Akkado-Elamite deities: A small and obscure group. This mainly was the Great God Ishtar, the Great God Sin written as 'Mano' or 'moon' in Bactrian within the Greek script.
In other words, the Kushan did adopt much of the Aryan traditions and customs, surely. However, there is also a level of diversity that is simply inherent to the Kushan monarchy and its outlook. It though, does not mean that they were indistinguishable from the Hindu, they certainly were, prior to the reign of Kanishka II, when the Hinduization of the Kushan southern kingdom reached a watermark.
Also, the Kushan operated in whichever language they needed for the moment. Inscriptions in the central region, were made in Bactrian and Greek. In the south, within languages of the subcontinent and in the northeast in Tocharian or Greek. The one excluded was the Pahlavi tongue of the nearby Arsacid empire of Eranshahr and certainly not Avestan. Greek appears on the majority of the coinage, displaying the importance relatively of Greek at least in the majority of the Kushan empire. Even after the fall of the main Kushan empire and the Kushan kings were lords only of the Indus and nearby Mathura, the Kushan kings still made their coinage in the Greek language or the Bactrian language with a Greek script instead of a Pahalavi script.