In some relatively secular or multi-religious Islamic countries, this is not the case, Indonesia and Turkey being some examples.
For a multi-ethnic, multi-religious country like Syria, without a strong leader the country would break up and we would have a civil war far worse than in Lebanon.
Myanmar (Burma) is a multi-religious country.
Ethiopia is a multi-religious country.
Serbia is a multi-religious country.
Iraq is a multiethnic, multi-religious and multi-sect country and Arabic and Kurdish are the official languages.
Sri Lanka is also a multi-religious country.
India is a multi-religious country and laws vary depending on the religion of the persons involved in child abduction/custody/access cases.
Vietnam is a multiethnic, multicultural and multi-religious country.
Although Kazakhstan is not a western liberal democracy in our tradition, it is making considerable progress as a multi-religious, secular, Muslim-majority country.