In a community having majority non-believers, do Muslims have to accept their (majorities) ruling or do they have to set their own different governance policy according to Sunnah, thus rejecting democracy and opposing the ruling government?

Democracy is not in line with the Shari`ah. The Islamic method of governance is to rule the state by Shari`ah. Many Muslims say that democracy coincides with Islam. This is not true because democracy is a man-made law and we are not allowed to set up governance with man-made laws. Democracy is not something which Muslims have to support. We are allowed to support the rule of Allah سبحانه وتعالى and we are not allowed to rule by other than the law of Allahسبحانه وتعالى. So, with regards to Muslim countries, they are not allowed to rule by democracy. The only way they are allowed to rule is by Shari`ah.

As for non-Muslim countries where Muslims are living in a minority and the non-Muslims are in the majority, in such a case, they do not have the power to establish the Shari`ah, rather they should do what is there in their capability, like building masajid and praying five times a day in the masjids. This is all a part of Shari`ah; however they cannot establish a government. What they can do is, they can ask the government to give them special courts in which they can establish some of the Shari`ah rules such as performing marriages and divorces according to the Shari`ah, and this exists in some non-Muslim countries, like England, where there are Islamic courts where a Muslim can go and get married according to Islamic law and get divorced according to Islamic law, etc.

And Allah knows best.