What is the legitimacy of the statement that the Islamic state is a civil state with an Islamic reference, and does this mean that Muslims and Christians are equal in rights, including nominating themselves for the presidency and building churches?

Islam does not deny the rights of non-Muslims residing in a Muslim state, but it differentiates between them and Muslims in specific rulings based on Islamic Sharia, which is the constitution of the state. Justice is giving every rightful person their due, not absolute equality, which might equate what should be differentiated. Equality might necessitate equating two things that wisdom dictates differentiating between, such as the differentiation in marriage between a Muslim woman and a Christian man, and prohibiting non-Muslims from holding authority over Muslims. It has been mentioned that Allah commanded justice, not equality, and differentiation in treatment does not negate justice; rather, it is a requirement of it. Similarly, it is not permissible to make patriotism a substitute for religion in judging people and equating Muslims and non-Muslims absolutely.