Question
Separation of the Church and State in Hinduism
Answer
This question can't be answered since Hinduism has no church. However, if this is a question about how a King should behave towards his subjects then it can be answered.
King must not be a tyrant
O king, thou shalt not swerve from virtue. Those men only, O Yudhishthira, whose practices resemble those of robbers, cause a king by their counsels to take to a career of war and victory. That king who, guided by considerations of place and time and moved by an understanding dependent on the scriptures, pardons even a number of robbers, incurs no sin. That king who, realising his tribute of a sixth, doth not protect his kingdom, taketh a fourth part of the sins of his kingdom. Listen also to that by which a king may not swerve from virtue. By transgressing the scriptures (one incurs sin), while by obeying them one may live fearlessly. That king who, guided by an understanding based upon the scriptures and disregarding lust and wrath, behaves impartially, like a father, towards all his subjects, never incurs sin. O thou of great splendour, if a king, afflicted by destiny, fails to accomplish an act which he should, such failure would not be called a trespass. By force and policy should the king put down his foes. He must not suffer sin to be perpetrated in his kingdom but should cause virtue to be practised. Brave men, those that are respectable in their practices, they that are virtuous in their acts, they that are possessed of learning, O Yudhishthira, Brahmanas conversant with Vedic texts and rites, and men of wealth, should especially be protected. In determining suits and accomplishing religious acts, they that are possessed of great learning should alone be employed. A prudent king will never repose his confidence upon one individual, however accomplished. That king who does not protect his subjects, whose passions are ungovernable, who is full of vanity, who is stained with haughtiness and malice, incurs sin and earns the reproach of tyranny. If the subjects of a king, O monarch, waste away from want of protection and are afflicted by the gods and ground down by robbers, the sin of all this stains the king himself. There is no sin, O Yudhishthira, in doing an act with heartiness, after full deliberation, and consultation with men capable of offering good advice. Our tasks fail or succeed through destiny. If exertion, however, be applied, sin would not touch the king.
Mahabharata Santi Parva Section XXIV
Maintenance of Social Harmony duty of a King
"Vyasa said, 'O thou of eyes like lotus petals, the protection of subjects is the duty of kings. Those men that are always observant of duty regard duty to be all powerful. Do thou, therefore, O king, walk in the steps of thy ancestors. With. Brahmanas, penances are a duty. This is the eternal ordinance of the Vedas. Penances, therefore, O bull of Bharata's race, constitute the eternal duty of Brahmanas. A Kshatriya is the protector of all persons in respect of their duties. That man who, addicted to earthly possessions, transgresses wholesome restraints, that offender against social harmony, should be chastised with a strong hand. That insensate person who seeks to transgress authority, be he an attendant, a son, or even a saint, indeed,--all men of such sinful nature, should by every means be chastised or even killed. That king who conducts himself otherwise incurs sin. He who does not protect morality when it is being disregarded is himself a trespasser against morality. The Kauravas were trespassers against morality. They have, with their followers, been slain by thee. Thou hast been observant of the duties of thy own order. Why then, O son of Pandu, dost thou indulge in such grief? The king should slay those that deserve death, make gifts to persons deserving of charity, and protect his subjects according to the ordinance.'
Mahabharata Santi Parva Section XXXII
A tyranical King should be overthrown
For fear of anarchy, Vena was made king, though he was not fit for it. Now that king himself has become the source of fear for the people. How can we secure the good of all beings?
Srimad Bhagavata Purana IV.14.9
A King will attain to joy in this world and the next, if he protects his subjects from oppressive officers and thieves, and collects taxes in accordance with the scriptural law.
Srimad Bhagavata Purana IV.14.17
Vena said: In the king is present all the Devas like Vishnu, Siva, Brahma, Indra, Soma, Agni, Varuna and all others who are supposed to bless and punish mortals. In fact, the king is the embodiment of all the Devas. Therefore, O Brahmanas, without further ado, offer your worship to me, the King. Pay my taxes without stinginess. Who is there to be adored other than myself?
Srimad Bhagavata Purana IV.14.26-28
When the Rishis were moreover insulted by the pretentious scholarship of Vena, and when they found that their noble prayer for the welfare of the world as a whole was rejected, their anger was aroused, and they said: Let him be destroyed, let him perish. He is by nature a perverted monster. To let him live is to allow the worlds to be reduced to ashes. An evil person like him deserves not to sit on the throne.
Srimad Bhagavata Purana IV.14.30-32
King gets merits or demerits
The King derives his highest good by protecting his people. A King who protects his people well, will derive one-sixth of the merits of his subjects in the life hereafter. But a King who collects taxes from people without administering their affairs properly, will lose all the merits to his credit and will inherit the sins of his people to boot.
Srimad Bhagavata Purana iV.20.14
Finally there is the issue of how people not belonging to the King's spiritual community should be treated.
The answer to that is given by the shloka given below.
If a holy act is against the interest of other members of the society, it should not be practiced. It is Dharma which is the source of Artha and even of Kama.
Kurma Purana I.2.54
The King should not favor his own spiritual system and not do anything that harms the interest of people belonging to other spiritual systems.
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