This article with the SR costume designer doesn't say anything about rubber suits, but does say they relied on Routh to fill out the suit with his body. It was material with sculpted rubber accents.
"This first look at Superman Returns
— due in theaters in June 2006 — shows that the skin-tight costume stretches over only the actor's muscles
and frame, without the augmented armored pecs or abs of recent movie superheroes...."
Spider Man had fake muscles, but they were still under cloth.