Virulence factors.
Strains that cause RF express M protein and N-acetyl-beta-D-glucosamine which produce the immune cross-reaction with myosin and lysoganglioside. M protein prevents opsonization and allows for more invasive infection.
Cutaneous strains lack these virulence factors and are thus not as invasive (nec fasc and toxic shock-like syndrome aside) and, naturally, won't produce the autoimmune response associated with those virulence factors.
Glomerulonephritis is just a result of immune complex deposition. There were two antigens associated with triggering the immune response: one was exotoxin B but I forget the other. These virulence factors are common to both strains of GAS.