Well I tried to do similar experiment with what DeeAnna did but using Sodium Citrate.
I'm not a chemist expert and just did what I thought it would be logical.
I have used two soap bars of the same recipe, but the second one was with 3% of sodium citrate on its lye water.
I cut about 1gr of each soap bar and diluted them in 4 jars that had 200gr of water each.
Looking at the next pic the two topmost jars had my hard tap water, and the two lowest deionized water, while the right jars had the soap bar with sodium citrate in its recipe diluted while the left jars the one without.
As I can see and understand, sodium citrate on a CP recipe doesn't affect at all how it will react with the specific amount of water. What I did next is to incorporate sodium citrate inside the right jars to see how it would affect the water.
The first one is showing the original dilution, the second when I added 5ml SC and the third one when I added 10ml more of SC.
It seems that as I was adding SC, the water was getting a little bit more clear, and few bubbles could stay alive for a while.
When I tested the two bars by washing my hand with my hard water, they both were lathering the same way showing many bubbles at the same time. The only difference I could see is that the bar with sodium citrate in its recipe had an average of bigger bubbles, as if someone was pumping them with air, while the soap without SC was making the same amount of bubbles but smaller in size.
I don't know if I did a "right" experiment or someone can make any conclusions upon using SC, so anyone can conduct me in doing another experiment.
So in contrary with EDTA, I feel that it needs more SC to get a similar effect of EDTA, but arises another question:
Assume that we use 4sodium EDTA or SC in our recipe of liquid or soap bar, can it work as a chelator and defeat all the hard water's minerals that are running plenty through our tap or EDTA is moslty used as a preservative, and SC as a "PH lowering agent"?