Assalamulaykum,
Contrary to popular belief, in Islam, minorites are supposed to equal rights.
I don't want to go offtopic, but here is a link which answer "Non moslems have no rights part."
Freedom of Belief & Minority Rights in Muslim Countries - IslamonLine.net - Ask The Scholar
However this is the most important part(s):
In Islam, freedom in its general sense is a well-established fact. At a time when people were enslaved intellectually, politically, socially, religiously, and economically, Islam came to establish the freedom of belief, freedom of thought, freedom of speech, and freedom to criticize. Islam strictly forbids that people be forced to adopt a certain creed or to believe in a particular religion. Allah Almighty says: [If it had been thy Lord's Will, they would all have believed, all who are on earth; wilt thou then compel mankind, against their will, to believe?] (Yunus 10: 99) This was in the Makkan era. In the Madinan period, Allah also revealed: [Let there be no compulsion in religion: truth stands out clear from error.] (Al-Baqarah 2: 256)
There are scholars who distinguish between apostasy on a personal level, which is not punishable by death, and apostasy that is accompanied by what we call today high treason, in which case the punishment is for high treason, not for apostasy.
However, some scholars do not distinguish between the two types. The issue pertains to the way of interpreting texts in the Qur’an and the Hadith that deal with that subject. A detailed answer to this question requires many more pages and Allah willing it will be made available in the future.
As for the second question, minority rights under Muslim rule is summed up in the rule “for them (minorities) are rights like ours and on them are responsibilities like ours.”
Furthermore, the Qur’an clearly protects the freedom of belief (Al-Baqarah: 256). It also protects the right of worship and respects all places of worship (Al-Hajj: 40).
On the outreach issue, the Qur’an does not forbid engagement in respectful and peaceful dialogue with others, especially the People of the Book, provided that neither side exploit the illiteracy or dire financial need of others so as to psychologically manipulate them in the name of outreach.
In brief, Islam believes in freedom of choice. Faith itself is a choice in Islam. The Qur’an states: [No compulsion in religion…] (Al-Baqarah 2: 256). All have the freedom to practice their own faith without harassment or any kind of threat.
The history of Islam proves this very well when Muslims, Christians, and Jews lived together in dominant Islamic societies. We can contrast this to the Muslims who lived in Christian Spain when they were persecuted and prejudiced against on account of their faith.
Second, anyone has the right to choose to convert to Islam or keep practicing his faith. But once a person converts to Islam, he should practice his faith and never change it. If he changes it, it is a major sin. Whether it is punishable by Islamic law is a debatable matter among Muslim scholars. Some believe he should be punished because they count this crime as betrayal, while others say that if someone changes his faith and does not challenge the Islamic society, they consider it a private matter between him and Allah and it is not punishable by the Islamic faith according to their view. However, both opinions agree that it is a sin punishable by Allah and that it is the worst form of sin.
As for minority rights, the Shari`ah protects the rights of non-Muslims living in an Islamic society. The Islamic state has to guarantee protection for their life, property, and the places of worship. The hadith states: “Whoever harms a non-Muslim (Dhimmi ) will not enter Paradise.” (Reported by Muslim)
As for spreading any other faith in the Islamic state, non-Muslims are allowed to teach their followers about their religion, but they are not allowed to go against the mainstream of the society.
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Now when I mean Islamic, It should follow Islamic law and the state of religion needs to be declared Islam.
However, nonmuslims also have their right of practicing their religion freely also.
Like, if nonmuslims are harassed in a predominantly Muslim community, how can they hear the true message of Islam? Obviously, it is important to clear up misconceptions.
However, nonmuslims need to realize that they need to abide to the laws of the land and must support the country in "hard times."
Allah Hafiz