Does umbilical hernia repair cause diastasis recti?

No. Diastasis recti is a condition where the rectus muscles gradually separate from the midline while the fascia remains intact. It is not a hernia. Umbilical hernia and diastasis recti can coexist and are not causally related.
Not usually. The diastasis recti is a separation of the rectus muscles of the abdomen as they move laterally (away from the midline). This causes a large buldge in the front of the abdomen especially when you sit up. The underlying fascia is intact, where a hernia is separated.