If I moved to India I would choose the political party that offered the most individual freedom.
If they based their ideology upon Hinduism and made constant references to it, no I wouldn't mind religious references in the least.
In exact point of fact, the Indian BJT Party does exactly that; they're Hindu nationalists, and their main problem is runaway family/demographic expansion of the Moslem minority, which is now up to 30% of India's population. The whole idea of dividing India and Pakistan was to keep the warring Hindus and Moslems apart, and now it looks like the Moslems might be able to force a second partition by the exercise of their genitals.
Over here, however, you're not allowed to take such things into consideration -- that's divisive and a thought-crime, especially for you, since you are one of them, the hated, suspect them who need to be watched, categorically criticized at every turn, and criminalized at every opportunity.
One does not have to pass a Christian-litmus test in order to be a Republican.