The way people perceive morality from religion is circular

Religious people often claim that objective morality can only be obtained from religion. Now, if you ask them why do they think that their religion is correct, one of their reasons will be that their religion has such good moral values and so on... but how did they come to the conclusion that those moral values are good? it is because they used their own inner moral values to judge the moral values of their own religion (empathy and so on) and that makes it a circular argument. Their only justification could be that they believe that those moral values from their religion are correct because they come from god. Then if you ask them what if their religion was exactly the same but somewhere it says "kill all people with blonde hair", would you accept that? If they say no then it's because it conflicts with their OWN inner moral values. If they say yes then.... 

In the end, morality has to be subjective in some sense because we always use our own inner moral values to judge "objective" morality. What do you think?