I’ve heard this claim before that it is not possible for atheists to have “objective moral beliefs” because many moral claims are based on religious authority, which atheists do not believe in.
Thus atheists are subjectivists when it comes to morality: each atheist may disagree with the other about what is moral. Obviously this opens atheists up to problems of disagreements, with some who might believe very conventionally “immoral” things are acceptable for them.
This is not of course to say that atheists may not choose to live lives that are some what “moral” (moral, as is often defined by religions)
So, what’s the status of the idea of “objective morality” and atheism?
One of the BIG questions in philosophy is whether morality can even be objective at all.
Your example religious morality is inherently subjective; it’s dependent on belief in the existence of a deity and adherence to their strictures. Athiest, due to the first part, cannot have religious morality but they often do adhere to other forms of subjective morality such as social, strategic, common, or pacifist; none of which require belief in a deity and have as much subjective validity as religious morality.