Tsuna

Well, hurray for that. Given that you didn't reply to my post, I'm assuming you're waiting on me to expand upon the arguments I didn't address due to confusion over your intent?
In that case...
Since you said I hit on your points well, then I'm going to address this:

Arguing the point that one is influenced regardless of personal beliefs, to put it shortly, transforms your argument from regarding one's individual concept of morality to an argument addressing the idea of nature versus nurture. Miburo touched on this in his earlier post:
Regardless of whether someone is raised in a religious environment, the capability of reason and logic is part of what makes us humans intelligent beings rather than mere animals who act on instinct. I could argue the point that as humans, we are not inherently primal by nature, but then you could also argue the case of Victor of Aveyron.

This is not a jab at your intelligence or lackthereof, but simply a clarification: If you don't know who Victor is, he was a feral child who had lived the majority of the first twelve years of his life in the wild, away from civilized society, only later to emerge from said wild into civilization. He was studied by a French biology professor, who observed him as being "close to the wild state of an animal". However, you can't really explore this case because Victor was virtually incapable of being educated, even so far as language - not because he was too primal to learn, but because he was deaf-mute, and unable to be taught.

Focusing on his feral-ness, now; given this example, you could say that though humans are capable of reasoning and logic, that regardless of said capabilities, it is the nurturing of said qualities that allows us humans to be "intelligent beings" who live by the rules of logic. But that's another debate entirely, and I'm drifting too far from the point.

The point is, the fact of one's morals being influenced by religion is the same as saying that the factor of human intelligence itself is based upon one's nurturing environment... For example, someone who is completely deaf may not be capable of actual spoken language (though they may use sounds to convey meanings at times, I have experienced) not because they are incapable of learning it, but because they have never been subjected to spoken language, and therefore have no means to learn it.

In short: Yes, because we live in civilized society where everything from laws to traditions to popular media are influenced by religion, whether or not we believe in said religion is void - we are surrounded by it from birth, it is in our schools, our governments, even the values of our respective societies as a whole, despite whether or not said values, governments, schools, or what so have you, are directly related to religious beliefs.

Although this is certainly true, one's personal beliefs need not have anything at all to do with religion. Even if one could argue that said beliefs have stemmed from religious backgrounds, that does not mean that one's moral system is irrevocably based on religion itself. This is where rationality comes in.

The fact of the matter is, just because we, as a people, are influenced by religion by nurture does not mean we are incapable of reasoning and morality in the absence of it.

See above.
Generally speaking, this is a valid point.
However, public opinion does not equal fact. Just because the majority of people believe something is true, doesn't necessarily mean it is.

Everyone used to believe the world was flat, until someone proved them wrong. They also used to believe that the Sun rotated around the Earth. But we now know it doesn't. Just because a "fact" is generally accepted as a truth doesn't mean it is definite.

This statement makes no sense. How can you be influenced by something when you aren't even aware of its existence?

The viewpoint as in the Western thing? Yeah, I agree, but not including that would leave it open for a counter-argument on the fact that those religions are really only more "recognized" in Western society. More specifically, in the United States. It's better to acknowledge a weakness in an argument based on one's personal experiences with their environment - i.e.: I only know the "big" religions as they are considered in the US rather than say, Russia, because I don't live in Russia, and thus don't know the situation there - than to just leave it wide open like that.

Maybe it's just the way I've learned how to debate over the years, but it's better to address all facets of an argument than to leave anything unexplored.

@ninja:
Protip: Agnosticism and Atheism are not even remotely the same thing.