Who decides morality?

*sigh*
You are conducting your argument from the position of assumed objective morality. That what we believe here and now is the objective standard that all past and future events must be judged.

This is fundamentally wrong. Morality is dependent on context.
There are arguments based on innate empathy that can be used to explain why certain things are possibly universally better or worse (which is why almost every society has had rules against murder, theft and perjury - but always qualified in the context of that society), but morality is still dependent on the society that supports it.
Slavery, sexism, etc is obviously not "objectively immoral" because there were, and are societies that consider them to be acceptable.

You need to stop thinking that a subjective morality becomes objective once it is held by a society. It is still subjective!

And yet, the reality is that atheists seem to find it easier to condemn actions that cause harm and suffering, while religionists often seem to have trouble rejecting such actions. Which is why we see these regular threads where religionists attempt to defend slavery, mass murder, torture, discrimination, oppression of belief, etc.

Perhaps it's because we have not tied ourselves to an arbitrary, brutal, ancient Middle Eastern morality and labelled it "objective"?

From what I have read, both you and QE2 accept that Nazi and ISIS culture has just as much credibility, support and justification as our western culture. Put simply, why is western morality better than theirs?

My point is more that atheists have no grounds for their condemnation, not that they are unwilling to condemn.

You keep telling us we think that. I for one do not believe it. ISIS, for instance, grounds its morality in the Koran which is a nasty book produced in the seventh century specifically to motivate people to act in order to further Mohammed's political aims. That morality is misogynistic, aggressive and pretty barbaric, and not suitable for twenty-first century use. It is, of course, an Abrahamic document and you would. I suspect, claim it to be within your objective morality. It is abhorrent to me (as are ISIS).

Our morality is better than theirs simply because it is more suited to our current society in the west, and to the way we, as a society, think and live our lives.

Of course we do. We make a judgement on the morality of an act and go from there. We certainly don't used an old book of fairy tales to inform our judgement and to think for us. I guess most modern atheists would not judge homosexual behaviour to be immoral, and certainly our society doesn't, so our subjective morality differs in detail from that of many religious people like you.

You might be better discussing with religious people why they don't follow the supposed objective morality laid down in the Bible. After all, many don't agree with what is written there, yet they claim to be believers in it and its message.

Everything in bold in you response is, in my opinion, an unfounded 'X is bad' value judgement. Who decides what is barbaric and misogynistic, or what is suitable for the 21st century? If it is just our culture then misogynists can just argue the opposite with as much effectiveness.

But if your judgement on the morality of an act is culturally-relative and based on unjustified value judgements, is it that more preferable than religious morality? Aren't both inadequate?

Society decides in the main, with scope for individual variation in some areas. Religious morality is, inevitably, ancient, outdated, unpopular, not suitable for modern western society and on the wane. So I suspect you are going to have to get used to common or garden non-religious morality.

We are still left with the problem of not having anything substantial to say against those with a different culture to us. Everything you have mentioned in bold is ran unfounded 'X is bad' statement.