"Rajput" is simply a title, not an ethnic group in the proper sense. They are somewhat similar to the Nayakas/Naiks that you find throughout India. There is no reason why a Muslim cannot call himself a Rajput, since the title 'Raja' is not exclusive to "Hinduism". The reason why Muslims historically have not done so, is essentially the same reason why white Americans don't adopt the titles of Native American chieftains. The Muslim upper-classes who dominated North India between the 13th and 18th centuries preferred to associate with Persian culture and use Persian titles rather than native Indian titles, which is why Muslim rulers used the titles Sultan and Shahanshah. Some of the weaker, local Muslim rulers (like the Sumrahs of Sind) used the title 'Raja', but they all aspired to be "Sultans" and "Shahs". Indeed, even the most powerful "Hindu" rulers, like the kings of Vijayanagara, also used the title of 'Sultan" (suratrana), as did Rana Kumbha. Neither the Indic nor the Persianate titles were exclusive to a single religion.
This is not about Rajas and Sultans.
Titles like 'Raja' or Sultan only stand for an individual and have never become the name of an entire community. That is not the case with 'Rajaputra/Rajput'.
Yes Rajputs are not one single ethinic group but Rajput is also not just a title. It is the term that identifies the progeny and relatives of Hindu Kshatriya Royals. Hindus don't have the patent on this term. Nobody has an any term. Muslims don't have on Mirza (used for Amber Kings). But anyway individual titles are not my point here. Community names are.
It is the Hindu Kshatriya identity that gave the Rajaputra term and not the other way round.
Rajaputra is the term that broadly replaced the term Kshatriya in north and central India.
By the time Gupta empire was disintegrating in 4th and 5th century AD, land ownership had become private, land grants and administrative posts were given on hereditory basis. Though Empire could re-assign as well.
The use of term 'Rajaputra' for people other than the current King's immediate son, first emerged in this phase only - for the extended progeny and relatives of the royal families (current and previous).
The term is found frequently in contemporary inscriptions.
(One of the very first recorded use of this term is for Buddha himself. Buddhist scriptures call him Rajaputra Siddhartha.)
The clan based Kingdoms that popped up from the ruins of Guptas, continued using this 'Rajaputra' term in administration just like their political predecessors.
Bana's Harshacharita mentions as 'Malava Rajaputra', the Malava king's two sons who took shelter in Thanesar - Kumaragupta II and Madhavagupta.
As the populations and feudal monarchies expanded, a number of princes and their progeny became feudal chieftains and kept using the title 'Rajaputra'. One example would be Kirtipal Chauhan of Nadol Branch of Chauhans. He was the autonomous King of a small Kingdom.
As we noted above that land ownership, grants and administrative posts had become hereditory Gupta onwards, the titles obviously turned to be used the same way.
Thus eventually the sons of Rajaputras came to be called Rajaputras only, as they inherited everything - from administrative power to land ownership.
To tell it more briefly :
Those of the Kshatriyas who were in the upper rings of State Administration held power, land and royal title of Rajaputra.
Later all the three turned hereditory, so obviously their progeny came to be called exactly what they were - Rajaputras.
Gradually the progeny expanded into an entire community that we know as Rajputs today.
As for the Muslim rulers, the post Mahmud Ghaznavid Sultans used the title of 'SamantaDeva' in their coins. Kumbha's title was 'Hindu-suratrana' .. not just Suratrana. Kumbha was called thus by Delhi and Gujarat Sultans who were defeated by the former repeatedly.
So yes individual titles were used interchangably, more liberally. But like I said before .. individual titles are not the scope of my argument.
People are free to decorate themselves by any term, who cares. But if there's a deeply entrenched identity associated a term, it doesn't carry over by merely grabbing the term. There's a reason why many Pakistanis in west call themselves Indians. Because they're looking to piggyback on the positive "identity" associated with this term. It may work in west, but doesn't work in India (host of that identity).
Regards,
Virendra