I'll bow to your knowledge of how Christianity views the soul, but this makes no sense from the Hindu or Jain philosophical viewpoint, which are more germane here since RJ lifted a lot of concepts almost whole cloth from those religions.

The soul can certainly gain enlightenment, and that is entirely a matter of your own effort, but to take that to mean nothing else can affect the soul is hardly a universal human belief. Some Hindu schools do believe the soul is untouchable and unaffected, but hardly all. And the non-dualist schools, which RJ seems to have drawn most heavily from, certainly don't think the soul is unaffected by other things.

The chief way the soul leaves itself open to influence, one which RJ came back to repeatedly, is in failing to realize that the world is an illusion, and that the soul is one with the rest of creation. This non-dualist view is clearly the source of Aiel, Da'shain and Amayar beliefs of life being a Dream/Illusion, and also the Oneness that allows channelers to access saidin or saidar.

As for rebirth, in Hindu belief, the cycle of rebirth is the way for the soul to gain salvation. To break free of the cycle, the soul must see its oneness with Brahman (which is what the True Source seems to be modeled on). Piercing through the illusion of reality to realize this is the way to salvation, and that's why everyone in WoT prays for rebirth and salvation.

Brandon Sanderson completely lost sight of these philosophical points, of course, so the simple answer to Rand and Ishamael's frustration with the cycle of rebirth was completely missed. But RJ left in plenty of clues that this is what he was going for.

And as a consequence, if the soul cannot be affected at all, there's no point to rebirth. The goal is to achieve self-knowledge through experience, which is impossible to do if the soul is hermetically sealed and unable to interact with the illusion of reality it is placed in.

Well he can do something about it. If he enters the world fully and makes it in his image, he can clearly do a lot with those souls. If they're so untouchable that he can't, his entry into the world wouldn't be nearly as scary, would it?

Ummm no... Trollocs were a product of human and animal genetics being mixed, sure, but it clearly wasn't a matter of crossing humans and animals to breed. RJ wasn't by any means a denier of evolution, and he wouldn't be so stupid as to violate speciation. In any case, we know Aginor was trying this with the One Power alone, and got severely condemned, then joined the Dark One to use the True Power in his experiments. It was not a simple matter of breeding.

But the bigger point about constructs is that they do bear souls at all. If the soul is untouchable by the One Power, this wouldn't be possible. Here's an RJ answer confirming it:

If you can borrow temporarily from the supply of souls awaiting rebirth using the One Power to create Nym (and Chora trees), that means the One Power can interact with and affect souls. There's no two ways about this.

No one said they can duplicate the work of Creation 100% (though who knows where they'd have taken their technology). But that isn't the question being discussed. The question is, can the One Power affect souls. Clearly, it can.

No. It is the ur-state of existence. As Verin explained to Egwene, it is the third constant, along with the Creator and the Dark One. To me, TAR is like the base substrate of creation. If your soul is able to project yourself there, you have Creator like powers (limited by your strength in the Dream). "Reality" is, basically, the Creators dream, melded to TAR (or dreamshard, as Brandon Sanderson called it. Stupid as that name is, I'll stick with it for convenience). Rand, in Shayol Ghul, was creating fresh Dreamshards in his contest with the Dark One, both of them re-writing the rules of reality as distinct from what the Creator has set.

Nope. RJ has said explicitly that it is their souls that go to TAR, awaiting rebirth.

It explicitly is not. Trying to change what the books to fit your worldview is a little bizarre, Cannoli.

Nope. Those are their souls.

We do. You're just ignoring it to make it fit your view of what souls must be. Which is deeply puzzling, since according to your beliefs, rebirth shouldn't be happening at all, yet that fundamental aspect of WoT you seem to have no problem acknowledging.

How do you figure that? The soul enters the world. It is affected by it. From how it deals with its experience, and depending on whether it achieves the self-knowledge to know it is in a dream, it is released from the cycle of rebirth, achieves salvation. Seems massively simple to me. Not sure why "nothing really does matter" if the soul can be affected by reality. I'd think the reverse is true. If nothing in reality can affect the soul, then what's the point of life, or, in the case of WoT, rebirth? Your argument would fit Ishamael's view, maybe, but not how most in WoT see things, or how RJ saw things for the world he created.

I do not see why the soul being something the One Power can affect is in any way affecting these things.

RJ's answer above contradicts this. If a soul can be corrupted so it can only be reborn as a Trolloc, then, clearly, the Dark One, at the least, can change your will.