How did Hobbes feel about religion being part of the government?
One should start out by noting that Hobbes' own views of religion are the subject, to some degree, of scholarly debate. He was definitely strong opposed to scholasticism and Roman Catholicism and trended toward materialism and rationalism in his overall philosophy. While he does argue that his form of political absolutism is compatible with Christianity, many accused him of being an atheist.
Within his objections to Roman Catholicism, as well as his dislike of what he sees as the metaphysical and nonsensical character of scholasticism, we see a political issue. Hobbes objected to the Church's meddling in national or civic affairs, especially in what he saw—as many of his fellow Englishmen did—as papal overreach in attempting to assert authority over governments.
Hobbes' political philosophy was based on the notion that the state of nature or anarchy is one of war of all against all in which life is "nasty, brutish, and short." In exchange for security, citizens enter into a social contract in which they surrender liberty to the monarch. This includes religious liberty. Religion is not a legitimate grounds for disobedience. The monarch, in fact, has the right to decide on a national religion. For Hobbes, religious authority was subordinate to monarchical authority and a national church, subordinated to the monarch, was an important part of establishing the peace and security for which the subjects had sacrificed liberty. In a time of violent religious wars, Hobbes was aware of religion's ability to create chaos and anarchy—the very forces he wanted to guard against. He thought, however, that Christianity might be compatible with order and absolutism, citing Jesus's belief in "rendering unto Caesar that which is Caesar's" as evidence.
In answering this question, remember that Hobbes's main idea is that the sovereign needs to have complete power over his subjects. This will tell you something about Hobbes's attitude towards religion in government. Hobbes did not believe that any church should have power in the government. The reason for this is that the church's power might interfere with or reduce that of the sovereign. Therefore, no organized churches should be able to wield power.
This is not to say that Hobbes believed that separation of church and state was necessary. Since Hobbes believed that the monarch should have complete power, he also believed that the monarch should have power over religion in the country. The monarch should be able to dictate what religious actions (as opposed to beliefs, which cannot be commanded) were taken or not taken.
So, Hobbes felt that churches should not interefere with the power of the sovereign, but had no problem with the sovereign controlling religion in his kingdom.