Are there any rules governing Muslims in relation to non-Muslims?

Answer 1

Yes indeed there are strong Islamic rules regarding every matter of lise especially how to treat the people of the conquered lands, people of other religions and state. Each one of them involves strong justice and rights of others. No community can harm any other community, take away their belongings or destroy their religious places. Islam is indeed the religion of peace but the modern media has the habit of promoting the dark side of it's followers.

Answer 2

The answer depends on whether we are discussing how Muslims as individuals are supposed to deal with Non-Muslims as individuals, how Muslim-led governments are supposed to deal with Non-Muslims as communities, or how Muslim communities are supposed to deal with Non-Muslim-led governments. (Q: means a Qur'anic verse that can be consulted to find clarification)

Between Muslims and Non-Muslims as people, Islam teaches its followers to treat those of different, but acceptable religions, such as Judaism and Christianity, with respect and cordiality. Q: 2:136-139. Friendships can occur between Muslims and Non-Muslims, but stronger connections such as intimate relationships are often forbidden unless the non-Muslim is a woman and she consents to have her children brought up as Muslims. Q: 5:5. If the non-Muslim is a man he is not permitted to marry a Muslim woman. If the religion is unacceptable, such as Hinduism or Buddhism, or the person is non-religious, the Muslim is supposed to ignore this person for fear that their beliefs will contaminate the Muslims' thought process. Q: 6:106. Of course, these laws are not stringently followed by everyone, especially in circumstances where Muslims find themselves surrounded by Hindus and Buddhists and would find it impossible to ignore them and so disdain the rule. Most Muslims as individuals find it far easier to follow the idea of tolerating other religions such as is in Q: 109:1-6. However, marriage would be out of the question. Q: 2:221.

Between Muslim-led governments and non-Muslim communities, there is usually a degree of segregation and increased taxation that is supposed to occur, as spelled out in Q: 9:29. Thankfully, most Muslim-led governments no longer engage in the outward actions that defined the Segregated or Dhimmi Status in earlier Islamic States, but there is still a general belief that Muslims should be the priority of a Muslim-led government and that unequal laws are permissible. For example, proselytization of any religion other than Islam is still prohibited in most Muslim-majority countries. Q: 1:6-7, 2:109.

Between Muslim communities and Non-Muslim-led governments, there is often suspicion. Muslims are generally loyal to their Non-Muslim-led countries of residence and have often served proudly in those armies and performed civic duties. However, the Qur'an makes clear that a Muslim should not be loyal to a Non-Muslim-led government. Q: 5:51. The exception to this is if a non-Muslim-led government rules in accordance with Islamic values. Q: 4:59.