I'll break down the answer into two parts for a more comprehensive coverage of the subject. The first part I shall try to make into a brief and accurate description of the Martial Race Theory both pre-1857 and post-1857, and in part 2, I shall specifically look at the Army of India in 1914-18 and 1939-45 to elaborate on how the Martial Race theory, shaped the composition of the Army.

"Martial Race Theory" : British Novelty? Or Continuing Tradition

A strange and prevalent misconception which has settled into both popular and academic approaches towards the study of British military recruitment policies in the subcontinent, perhaps owing in some part to early nationalist historiography and in other, the presumption of an underlying "apparent truth" behind popular conceptions of historical phenomenon, responsible for sustaining theories in popular history otherwise incongruent with academic consensus, known commonly as "common sense", is that the Martial Race Theory was a British invention, manufactured for creating fissures in an otherwise harmonious "Indian" society which in the long run created those communal tensions responsible for horrific incidents that shaped Indian history in the late 19th and 20th century. We find upon interrogation of secondary sources, existing research and historiography on successful pre-British military systems in the subcontinent that selective recruitment from historically "militarised" classes and castes has been a common feature of the many armies and polities in the subcontinent.

From, Ali. Athar. M. The Mughal Nobility Under Aurangzeb, 1970, p. 11-15 :

A very interesting description of the composite nature of the Mughal nobility is given by Chandrabhan Brahman, who wrote during the last years of Shahjahan's reign :

From different races, Arabs, Persians, Turks, Tajiks, Kurds, Lars, Tartars, Russians, Circassians, Abyssinians etc.... and various groups of Indians, men possessed of knowledge and skill as well as men of the sword viz. Bukhari and Bhakhari, Saiyids of correct lineage, Shaikhzades of noble ancestry, tribes of the Afghans such as Lodis, Rohillas, Yusufzai etc. And clans of Rajputs styled rana, raja, rao, and rayan such as Rathors, Sisodias, Kachwahas, Haras, Gaurs, Chauhans, Jhalas, Chandravats [etc.]... and all other people of India, such as the races of Ghakkars, Langahs, Khokars, Baluch and other races, men of the pen and the sword, holding the postions of 7,000 to 1,000...

Furthermore, from, Gommans, J.J.L. Mughal Warfare: Indian Frontiers and Highroads to Empire 1500 1700, 2002, pp. 85

For this purpose, Akbar revived the system of horse branding (dagh), which had already been in use during the Delhi Sultanate. Apart from registering the horse’s breed, colour and marks on its body, etc., each and every horseman was also described in rolls (chehra), which laid down his name, father’s name, tribe or caste, place of origin, complexion, features, any identification marks, stature and age.

From the above illustration the intention is to state what Prof. Ali so graciously does in his comprehensive volume, that the Mughal military system was both conscious of and took prejudice with regards to the distinct social and ethnic divisions which pervaded North Indian society and that of it's neighbourhood. From among their Hindu subjects, Rajputs, Kayashtas and Brahmins were recruited as according to their perceived "qualities" as "races" or "groups", and both Kayashtas and Brahmins along with Rajputs acquired incredible positions and favour in military service though the latter clearly dominated the Hindu Mansabdari of the Mughal Era. The zamindars of the various Subahs and Sarkars ( Provinces and "districts") similarly reflected this social heriarchy. For example, on page 190, Appendix D, from the Subah Of Allahabad Under The Great Mughals, 1974, of S. N Sinha :

Of the 53 recorded zamindaris : 10 are Brahmin, 12 Rajput, 3 Gaharwali , 1 Bhar, 1 Kayashta, 1 Birasi, 1 Kurmi, 1 Bachgoti, 1 Baoria, 3 Khandwal, 1 Bisen, 2 Parihar, 2 Gond, 2 Bais, 1 Bagri, 1 Chandel and 3 are various castes.

Other than this, there's 1 Rahmatullahi, 1 Turkman, 1 Siddiqi, 1 Faruqi, 1 Ansari, 1 Saiyid and 1 Afghan Lodi.

It has further, been repeatedly stated by Muslim court chroniclers that indeed since the times of Alauddin Khilji, the overwhelming majority of landed gentry in Hindustan, was upper caste Hindus.

We find a similar sentiment prevalent in the recruiting policies of the Army of Hindustan of Mahadji Scindia, as on p. 120, of The Military System Of The Marathas, 1928 by Surendra Nath Sen, we find that the recruits for their famed regular infantry batallions, were drawn from Oudh with a rich supply of mercenary castes, that were known as Purbiyas, or Telingas, as well as Rohillkhand, whose stock was referred to as Najibs. These regions, had supplied military labour in North Indian armies since the early centuries of the 2nd millennium CE. As Dirk H.A. Kolf shows in his Naukar, Rajput and Sepoy, 1990, p. 159-170, that the North Indian military labour market, was by and large monopolised by these highly militarised upper caste mercenaries from Oudh and certain districts of the Bhojpur region, largely composed of Brahmins and Rajputs.

Therefore, when the company in Bengal, which had until 1757, not required the raising and maintenance of an armed force to protect it's existence on land, its factories and ports, was forced into a desperate situation to call upon available resources and muster a body of soldiers, they naturally looked to these very same established stocks of fine and proven soldiers and mercenary men. Put simply, their preferences and decisions with regards to recruiting policy, were informed not merely by the contemporary conceptions of "temperate" and "colder" climates which produced different races, unequal in matters of warfare, but also by the existing precedent of military systems, and the availabe military labour pool, which made obvious the optimal choice for a potential recruit.