So you haven’t found any connection between Bentham’s and Mill’s utilitarianism and Christianty. I assumed that you looked and have come up empty. So I will just repeat what Insaid before with no fear of contradiction: It is not based on Christianity.
So we have various moral codes apart from Christianity. Atheism isn’t one of them. Atheism is a lack of belief in gods. So what we can say is that any moral code that an atheist is likely to follow does not rely on a belief in God. But that he or she may well concur with teachings that Christianity also recommends. Like the golden rule for example.
There are a few atheists who regularly post in this forum. And I will absolutely guarantee that we don’t follow the exact same path when it comes to morality. That would be akin to saying that all Christians do.
If you want to know what atheists think about any moral position then there is no atheist scripture to which you can read. There are no atheist priests to whom you could refer. You might find this a little surprising, but if you want to know what any given atheist thinks about any given matter, then you are going to have to ask him.
I know what position you have on ssm. Or abortion. Or contraception. Or sex outside marriage. Or rather I know what position you are meant to take. If you want to know mine, then feel free to ask. I will also be able to give you the reason why I hold to a particular belief. Will you be able to do the same? If you can then we can discuss them. That’s what a forum is for.