I think I have answered this before. I think everyone on this planet believes that their morality is correct. Otherwise they would think otherwise. Hence it is probably fair to say that for many people morality is subjective. Most people - if not all people - decide for themselves what they believe is right and wrong. I say this was the result of eating the forbidden fruit. We as a general rule are not content to believe that someone else - In particularly God, can decide what is right and wrong, we want to do it ourselves after having thought about it for a while, using whatever source we so decide is the correct one. Hence secularist think such things are decided by reason or evidence they see, others look to a holy book, others to intuition, others to the starts etc. Of course, if morality is truly subjective - then all of these sources must be correct, because that is the nature of subjectivity.
Yet, once we start down the path of pure subjectivism, we soon realise the idiocy of such a journey. After all, if morality is truly subjective, then no one really has the right to suggest that anyone else's morality is incorrect, wrong, bizarre, or odd. Everything is permissible. Yet we could not live or function in such a society. There could be no rules or laws or ways to enforce such rules. What is mine suddenly becomes everyone else's who wants it and likewise - life and human rights become nonsense.
So practically, it could not work to really have subjective morality - despite the fact that many people are drawn to it. Once people are themselves confronted by it - and it hits them personally - they tend to take a less subjective point of view. All communists I know - lose full identity with communism when I ask for the money in their wallet or to sleep with their wife. Why? Because suddenly people move from subjectivity to wanting to rely upon a more objective position.
So I think the question of morality is more complex that asking whether it is either / or subjective / objective.
It appears that all people take the view that morality is subjective personally. Yet we all in general accept that there are seemingly objective principles which are necessary in order for society to function properly. On one hand we all want to be philosophers and be all wise - and on the other hand we want to be scientists and nail down every objective fact. Science requires hard objective facts. Philosophy does not. Morality seems to be a mixture of both.
This is why I am happy to conclude that God's subjective morality is objective morality for the rest of the universe - while acknowledging that every person is going to subjectively do what they think is right or wrong. But something are always wrong. there is no right reason for an adult human to have sex with a two month old human. There simply is not any right reason to do so. Yet people do it - tragically and I would add evilly. And I don't think that there could be any good justification for doing so. You might take a different view.
I suppose we could speculate. After all, what good reason was there for dropping a nuke on Japan? To end the war. To save millions of lives. The end justifies the means. Utilitarian morality. An alien might say to an adult male - how much do you love this world? Would you rape this child? and if you do so - I will spare the world from extermination. Would that be justification? I would say no. But I dare say - some might think the end justifies the means.
but that is the difference. Morality. What is it based upon? How do we measure it? I could say - that without God people cannot be moral. But all of the non- theists would jump up and say - we are moral people. Do they mean subjectively or objectively? How do they determine that morality? According to whom? or what?