listen to me, sahib,' said the taller fiercer of the pair, the one they called Abdullah Khan. "You must either be with us now or you must be silenced forever. The thing is too great a one for us to hesitate. Either you are heart and soul with us on your oath on the cross of the Christians, or your body this night shall be thrown into a ditch and we shall pass over to our brothers in the rebel army
o
the thing stands, Sahib, and I tell it to you because I know that an oath is a binding thing upon a feringhee, that we may trust you. Had you been a lying Hindoo, though you had sworn by all the gods in their false temples, your blood would have been upon the knife and your body in the water. But the Sikh knows the Englishmen, and the Englishmen knows the Sikh. Hearken, then, to what I say.
As a religious minority, Sikhs have for most of their history generally been living under non-Sikh rulers, such as the Muslim Mughals, or at least as part of a non-Sikh majority state. Thus, they often had poor relations with Muslims or Hindus who they felt treated them badly.
Like many colonial Empires, the British used a divide and rule policy in India, putting minority groups in charge to ensure their loyalty. One of their favoured groups were the Sikhs, who were especially favoured as soldiers (if you look at pictures of 19th century British Raj soldiers, there's a lot of Sikhs, and indeed in post-colonial India Sikhs still took up a disproportionate percentage of the army). Sikhs were also rewarded a lot more with honours than Hindus or Muslims.
Essentially, the argument to the Sikhs was "Better to be a 2nd class citizen in a country where all Indians are 2nd-class citizens, than a 2nd-class citizen in a country where the Hindu/Muslim majority are 1st class citizens." Basically, it was argued that a Hindu or Muslim ruler would put Hindus or Muslims first, while Christian rulers would be fair (as the number of Christian Indians was very small). Now, one might argue that Sikhs were Indians, but at the time, for a Punjabi Sikh, a Tamil or Gujerati or so on, was just as foreign as a British Christian.
Now, this is not to say that the British treated the Sikhs excellently. They were subjects of the Empire, far below the British. Sikh areas suffered from the same unfair economic policies as Hindu areas. It was primarily Sikhs who were the victims of the Amritsar Massacre, which showed not only British brutality but its disrespect for the Sikh religion (one of the reasons for the massacre is the British general didn't realise that the day he'd banned Sikhs from visiting the city was the day of Vaisakhi, an important Punjabi harvest festival and also an important Sikh religious festival). So, I think Doyle is probably showing the bias of a Victorian. To the Victorian understanding of India, Sikhs and Hindus hated each other, but Sikhs were loyal to the British because they were grateful for the favoured position (of fighting and dying as soldiers) that the British had kindly given them. They recognised the virtue of the English Christians, compared to the perfidy of the Hindoos and Moslems. Thus, it makes perfect sense that a Sikh would trust a Christian but not a Hindu.
In reality, while there's an element of truth here, it's not quite so simple. Relations between Sikhs and British, while at times better than those between Muslims and British, were hardly perfect, and relations between Sikhs and Muslims and Hindus, while historically tense, were not so bad that no Sikh would trust a Hindu. They did live alongside each other to some extent, after all.
It's important to remember the British had a habit, due to both bureaucracy and racism, of simplifying Indian ethnicities, polities, religious divisions, and of course castes, and the relations between them. And in doing so, they often exacerbated such divisions.
A clarification on the question: Isn't Abdullah khan a muslim name? Could it be that Conan Doyle was confusing Pathans (Afghans) with Sikhs? (similar head gear and such, but different majority religions: Islam vs Sikh).