Most atheists recognise and accept that values like "human rights" are human inventions, social constructs that are entirely abstract and do not "exist" in the sense that there is some innate value baked into the universe that imbibes human beings with certain attributes. However, constructs, ideals, and values such as "human rights" are a way for people to apply the ideas kindness and compassion is practice. We can (mostly) all recognise that all humans (and many animals) are capable of experiencing suffering, and empathy (which is something that almost all humans are capable of) compels us to alleviare that suffering.
In other words: human morality and ethics is an entirely abstract invention that doesn't exist outside of the human mind, but applying this invention to our societies is mutually beneficial and improves the lived experience of all concerned (well, theoretically, at least).