Atheists such as myself say that moral absolutes don't exist because a moral absolute would mean universal condemnation of 'absolute morally wrong' behavior, and that just doesn't exist. The fact that there are people who do not view rape as morally incorrect behavior means it's not absolute in the universal sense.
Does the lack of moral absolutes mean morality is therefore arbitrary? Of course not. Atheists have a number of meta-ethical systems which describe their criteria for judging moral behavior. Such as
utilitarian consequentialism, which analyzes the consequence of actions to determine help v harm.
[Incidentally because you didn't specify human on human rape, I don't consider non-human animals raping eachother or even non-human animals raping humans to be morally wrong behavior for them, as they don't have the intellectual framework to analyze the consequences of their actions and are thus, blameless, only when considering the harm rape does to adult humans by other adult humans do we determine moral fault.]
This is in contrast to dogmatism and divine command theory which only holds that what you're told is moral authority. Which I object to for a number of reasons:
First and foremost, I don't believe god(s) exist, which means the moral instruction Christians receive is just as human based as mine and therefore not divine. But more importantly,
I'm not an authoritarian, I don't believe command, instruction or law, divine or otherwise, is sufficient to establish moral judgement. If a powerful person or entity claims to have my best interest at heart, and that's why I should have faith in their instruction, I would not take it at its word and. Instead, I would analyze the consequence of the instruction I'm given to determine help vs harm. Thus I could never equate what is morally good to being what is commanded by a god or gods.
I don't believe Christians (or any religious person) have objective morality, with no subjective input. Moral instruction from their religion must be filtered through a number people's interpretations. The subjective view of the deity, the author of the scripture, the translator of the scripture, the reader and religious organization's input (if not non-denominational). All these filters add individual and subjective meaning.
I don't believe Christians (or any religious person) doesn't have moral autonomy. This is shown by brain scanning studies which show consulting one's personal moral compass is the same as considering 'What would Jesus do,' meaning religious people superimpose their own moral judgement on their religion and that they are informing their moral judgement, not the other way around.
Believers' estimates of God's beliefs are more egocentric than estimates of other people's beliefs
Creating God in one's own image - Not Exactly Rocket Science
Dear God, please confirm what I already believe
Further, here's a handy video series talking about atheistic morality which goes at length and far more eloquently than I can: