Steel strings categorically did *not* replace nylon, and cat gut has *never* been used to make guitar strings (except maybe by some cat-hating mountain man). Gut strings (and gut frets) are, and always were) made of sheep guts (or sinew). Cat gut is not strong enough for an instrument the size of a lute or guitar, although it was apparently used on some smaller Spanish instuments in the 15th to 16th centuries that were sort of a cross between a mandolin and a ukelele.
Steel strings first became available in 1900, originally for banjos, but they were adapted for guitars by Christian Martin. The fan bracing in state of the art Spanish guitars of the time did not support the stress of steel strings all that well, but Martin increased the size of the X-bracing in a number of guitars, as well as developing larger bodies (dreadnought type) to make an instrument compatible with ensembles involving louder instruments, including early precursors of jazz and bluegrass.
Martin's steel string guitars were a standard by the 1920's.
Nylon was invented by Wallace Carothers, a Dupont chemist, in 1934. It was patented in 1935, and was not released until 1938, primarily as a replacement for Japanese silk for parachutes. It was soon applied to women's stockings. Rationed during WWII for milltary needs, nylon was not applied to guitar strings until 1946, when restrictions were lifted-Richie
Note- Carothers never lived to see his success. He comitted suicide in 1937.