Can I backtrack here just a second, since this was originally about the Geth having souls? I'm just finishing up ME2 and got Legion not long ago. From what I can tell, he's still a networked AI. There's a bit about him being "special" but it was hard for me to tell from the dialogue just how special, but he can't operate on his own, right? He specifically says that the Geth can't function without being networked.
Did something change between ME2 and ME3? Because if they have to be networked, then they still share everything. I am myself because I have my own thoughts, memories, feelings, and emotions. All of those things make me, "me." If I do have a soul, it's my soul. It's not shared. If the Geth can't function outside of the network, how can it possibly have a soul, in any sense of the word, unless we want to start talking about shared souls, and that's beyond the scope of what I can think about tonight.
Legion has enough programs in his hardware to operate independently. Consider him a Geth 2.0. Geth would not normally create such a thing, as they are quite comfortable with their Consensus, but this was seemingly done in order to figure out heretics/organics/Shepard.
The Geth are programs. Each program can be considered a single Geth. Many programs go into a Geth platform, networking with the Consensus, and gaining the intelligence in order to ask, say, philosophical questions.
So what's happening here is that the single Geth platform is designed by the Quarians to be just a really good super-tool, but the platform is starting to 'think' it is an 'individual', if only barely. That the platform it is in, or rather the specific programs it houses, is a 'person' who very well could have a 'soul'.
So indeed, if Geth have souls, it is a concept that is beyond most human understanding. Is the soul the single programs? Is the soul the Consensus itself? Is the soul the specific combination of programs within a single platform that combined with Consensus intelligence may start to view itself as a single person?
Legion is basically the furthest example of the latter, making him the easiest to 'relate' to as a 'person'. He then goes even further in ME3, having gained supposed insights from networking with the Reapers (... consider that a good or bad thing), and deciding, 'individually', that a Reaper code upgrade is an ideal course of action for the Geth. That they can use this upgrade, on their own, still be free as a 'people', and become more than anyone could have ever imagined. The player can decide whether this is right or wrong to do, and decide whether Legion is actually in his 'right mind' or instead gone 'insane' from Reaper exposure, but it is Legion's position nonetheless and we have to do something about it because the Dyson Sphere path for the Geth was destroyed by the Quarians.
If Legion performs the upgrade, it seems like the Geth become even more like 'individuals' than ever before, able to see their platforms as their bodies, while also being able to transcend the body in their Consensus. Basically they've achieved everything they wanted to achieve, and we have to decide whether we're comfortable with this, given that it was achieved through assets and aspects of the Reapers, instead of the Geth alone. It isn't necessarily like Geth/Legion accepted any single Reaper's 'path', but Legion did take the path of 'The Reapers'. Through this, they seem to have acquired what appears closest to 'a soul'. Though I find it funny and interesting that many players actually find this version of the Geth/Legion to be disturbing, and only consider ME2 Legion, if anyone, to be 'someone developing a soul' on their own, and that the Reaper upgrade actually 'corrupted' the process, in a way.
Your position on the soul is like I expressed in a previous post - it is singular. It is also a very anthropocentric view on the soul, and one that at least has bias towards only human beings having souls, not animals, tools, objects, non-sapient or non-sentient organic things, etc. There are other spiritual views that actually go far beyond humans, and may even include every single thing in all of existence, but it is more comfortable for many people to not call this spirituality 'souls' but instead 'essence' or something like that. A lot of this is from our association of the soul as something one 'owns' (instead of what one 'is') and that is can be sold/taken. That is it an 'object' in itself, not an expression ('to soul', heh). To the Geth, one doesn't 'have' a soul - one, if anything, 'is' a soul. Maybe. They're not sure yet. But I think what ME3 tries to make clear (whether one considers it good writing or not) is that 'Does this unit have a soul?' is an unresolved question for the Consensus, one that sees the Quarian writings of 'having' a soul but cannot reconcile that with their state of existence as programs.