Hello
Having attended a mainly sikh school here in London many of my friends are Sikh and want to be pilots and have Parents or relatives who are Pilots.
I know Air India Definetly allows it as I believe they have a number of pilots who where thier turbin safely, also there are many Low cost start up carriers in India now so it might not be a bad Idea to get back to your roots and work for one of the Indian carriers Since you are of indian origin they will look at you favourably especially if you have the experience which obviously you have.
The British police and Fire Brigade services here have many Sikh people and I know some of them and they can carry out thier duty just as well with thier turbin, I mean many of the british carrier will have a compationate view to religious beliefe and try to care to those needs, British Airways is one and then you can try out other carriers like BMI or Virgin, so you have many Ideas but if you really want to stay in the USA, then you might try flying for the lost cost carriers rather than the Big boys or even better maybe get a Air India Job that is Based in the USA but am not sure if AI flies to the USA, better still they do fly to the USA as my uncle has been there using Air India. You options are open just contact everyone your interested in, and hopefully you will succeesed so best of luck.
Kind regards
AIRLEBANON