19th century Sikhs seemed to have had an abhorrence to wearing caps or hats rather than turbans in military service as part of their religious beliefs.
Their uniform is after the French fashion, scarlet coaties, with green lapells, and worsted epaulets, black belts, tight breeches, and gaiters buttoned to the knee. The head-dress is a turban, as nothing could overcome the prejudice against a hat or cap. (Asiatic Journal, 1839) 
‘however, the more closely-fitting dress of an officer belonging to one of the Maharajah's regiments pointed out that European customs had been adopted to some extent, but the existing head-dress of crimson or other bright coloured silk still attests the unwillingness of the Sikh soldier to wear the chako’ (Barr, 1844) 
Although they had strong views against wearing military hats such as the shako (a tall, cylindrical military cap typically worn in British regiments), they seem to have felt differently about the wearing of helmets.
A fascinating insight into the thinking of 19th century Sikh soldiers survives in the form of a letter between Henry Lawrence, the Resident at Lahore, Agent to the Governor-General and his correspondence with Lord Hardinge, the British Governor General of India. At the time Lawrence was trying to recruit Sikh soldiers in the British Indian Army following the first Anglo-Sikh War:
‘I have talked [he says in March 1846] to several men as to their entering our service. They at once said they would be delighted, and would go wherever we liked; but that they hoped we would allow them to wear their hair and turbans. The hair, I observed, would be respected, but turbans could not be allowed. After some talk they said there would be no objection to helmets or caps of iron. I thought that this would help us out of the difficulty, and I hope that your Excellency will approve of the idea, and authorize me to say that iron or steel caps will be permitted, and that their hair will not be interfered with....The Sikhs say that, according to their holy books, any man who wears a cap will suffer purgatory for seven generations, and a Sikh would prefer death to having his beard cut.’ 
The Sikhs soldiers that Lawrence encountered seemed to have differentiated between wearing a steel helmet and a hat, regarding the former as permissible, while the latter as unacceptable as per their 19th century interpretation of Sikh religious beliefs. It is important to note that this attitude towards wearing helmets was specific to that time period of the early to mid 19th century only and was not carried over into the post-Sikh Empire days of the British Raj. Following the annexation of Punjab and the integration of Sikh troops in the British Indian army in the latter half of the 19th century Sikhs were allowed to wear their turbans and did not have to wear helmets.
At the advent of World War I as they fought in the trenches of Europe against the Germans, the British authorities tried to persuade Sikh soldiers to wear helmets, something they refused to do and they wore their turbans through two World Wars as part of the British Indian Army.
1. "The Kingdom of the Sikhs", The Asiatic Journal and Monthly Register, Vol. XXVIII, Jan-Apr, 1839, 90
2. William Barr, Journal of a March from Delhi to Peshawur (London: 1844) 112
3. Herbert B. Edwardes, Herman Merivale, Life of Sir Henry Lawrence (London: 1873), 387