Calcium phosphate stones are actually pretty rare. While calcium oxalate stones comprise about 80% of all instances of nephrolithiasis, calcium phosphate stones typically occur only in a small subset of patients--about 5 to 10% of patients according to this source. In particular, calcium phosphate nephrolithiasis is encouraged by an alkaline urine. Thus, three conditions in which calcium phosphate nephrolithiasis may commonly occur are distal renal tubular acidosis, primary hyperparathyroidism, and milk-alkali syndrome.
In patients with distal (type I) RTA, there is a direct effect of acidosis which decreases renal calcium reabsorption; in addition, acidosis stimulates bone resorption (which increases serum calcium and phosphate levels) which can contribute to supersaturation of calcium and phosphate in the tubular lumen.