Chlorine is not going to affect your buffers - the buffers react to the acidity/alkalinity of your water. Not chlorine.
Municiple water supplies typically have around 1 mg/L free chlorine in them, they are allowed up to 4 mg/L in the US. That's 1/1000 gram in one liter of water. That is not a whole lot. If you developer has any sulfite in it, it will react with the chlorine and neutralize it. And I think your developer has some sulfite. So I would look elsewhere other than chlorine.
If you developer doesn't have much buffering, then look at the alkalinity of the water. You can check with your local water bureau to find out what the typical values are for your city.
If you are in Los Angeles County, not City, look here:
For example, the City of Lomita has an alkalinity of 92 in 2003, not too high, but not low. pH of 8.2. That level would have no affect on a low pH developer like XTOL. Chlorine level was 2.5 mg/L. So not very high.
I suggest you look to other causes.