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.