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?
Well but so what’s to moderate disagreements between Atheist A who believes one thing is right versus Atheist B who believes some other opposite thing is right?
Atheist C
The same things that moderate disagreements between members of one religious sect that believes that God commanded that this is right and members of another religious sect that believes that God commanded otherwise - persuasion or force (and the latter either done directly or through a legal representative proxy).
There are no short cuts anywhere in morality - it all always comes down to what individuals believe, how many others share those beliefs and how far the believers are willing and able to go to force others to submit. Various approaches to it work better or worse in various settings and among various participants, but it’s all the same basic dynamic, always.
For example, it could come to be commonly held in a particular civilization that religious morality is inherently flawed - the claims made by an evil church, or even the claims made by a false god - and the only legitimate source of morality is human reason. And if that view was sufficiently widely held, then that would be the reality for that civilization.
And then it could even be the case that someone in that civilization could post on a message board one day, wondering how theists manage.