Consider the following though.
We know, from the quest Ysera sends us on, (which I have discovered is called “From A Dark Place”) that we are able to identify souls, even the faceless, spectral variety we sometimes find in the Maw, which is how these souls appear during this quest. Otherwise, we as characters were asked to find Night Elves, and just happened to grab a few that were Night Elves by sheer dumb luck. Therefore, even if we as players cannot tell specific information about these souls, are character, as presented in the story, can.
Now, this presents two options for our characters: when soul collecting, they are either biased, or they are unbiased. This is is simply the logic of you are something or you are not. They either collect souls completely randomly, or they have some reason for collecting souls. We cannot be certain, but again, as established in this quest, our character has the ability to discern traits about the soul that allows them to pick them out, even if we as players see only empty, faceless wraiths. Therefore, we can only speculate whether our character are biased or not, and if so, what that bias may be.
Now consider this. The story, as told, has shown our character to have certain views and biases. For one, our character is allied with our faction, and thus, opposed to the other faction. Enough to fight in the war, as is established in the story of Shadowlands within Bastion, as we see one of the acts of service is your character fighting the other faction.
Whether this ability to fight was born out of hatred for the other faction, or self defense, or a desire to protect your people, the result was that you ended up killing the other faction and defending your own.
Now, in my perspective, this seems like a strong enough bias to cause a character to continue to hold to these habits, and favor rescuing souls of their own faction over others. True, we cannot know this for certain, but we also cannot know for certain that they are being random and unbiased, and thus all we can do is make an educated guess based on the evidence.
Again, in my opinion, based on the evidence presented, such as our loyalty to our faction (our character is, presumably, loyalty to their own faction, or at the very least more loyal to their faction then they are to the other factions), it seems likely that this bias would affect who they took home, such that an Alliance players sanctum would at the very least end up with more Alliance souls then Horde souls, and vice versa.
Again, we don’t know for certain, and it may be possible that, in this expansion, Blizzard decides to paint our characters as completely fair and unbiased, but I believe that is simply less realistic than assuming they would play favorites.