For example, I am writing "The Christians and the Muslims are equal in numbers in Bosnia." Can I also write "The Christians and Muslims are equal in numbers in Bosnia" or "Christians and Muslims are equal in numbers in Bosnia"..
will in my opinion it depends on what do you mean with it if you sat Christians and Muslims are then you mean every Christians and Muslims but you can say the Christians and the Muslims in America so if it is specific situation you use the if it is in general you don't use the at all
and i think the difference between the Christians and Muslims and the Christina and the Muslims i think it changes by what you mean because if you say the first one with only one "the" then they share something in common but in second sentence with two "the" you mean they are different they don't share something in common but you wanted to mention them in the same sentence that is my opinion i