Why does Calcium Carbonate inhibit the Citrate buffer system?

Any acid buffer (pH <7) will react with calcium carbonate.
This reaction will first reduce the buffer capacity, then the pH of the solution will rise and finally, poorly soluble in water calcium citrate (solubility<1g / L) will precipitate.

Calcium is calcium, calcium carbonate is calcium carbonate. Sounds like you are using them interchangeably as if it was the same thing and same process in each case.

It is not.

 AWK- Since citrate is specifically a chelator of calcium, will this have an additional effect? If so do you know of any resources that explain this chelation process?
 If using citrate fertilizers to maintain a pH in soil, would a high concentration of calcium in the soil thus inhibit this? Thanks!

The citrate buffer has a range of action from pH = 3 to pH = 6.2. The calcium cation binds very poorly to the citrate, and chelation is also very pH-dependent. Soil is a buffer system. Humic acids complex calcium cations, and this is also pH-dependent. Just measure the pH after mixing with the buffer and everything will be explained. If the pH is significantly different than expected, you need to increase the buffer capacity of your citrate buffer.