"The distinctive prison stripes were abolished in 1904. …stripes had come to be looked upon as a badge of shame and were a constant humiliation and irritant to many prisoners' (Report of the New York (State) Prison Department, 1904: 22)"
Pratt, John Clark (2002). Punishment and civilization: penal tolerance and intolerance in modern society
Now, that wasn't a hard and fast rule, as North Carolina kept the stripes until 1958, but the stripes were becoming passe due to a changing attitude regarding non-violent criminals becoming the majority of inmates.
Following that, most places in the US switched to denim-style work clothes, or khaki in the federal system, which is still somewhat in use today.
Even today, the orange jumpsuits are not ubiquitous. New York state actually bans the color orange among prisoners: It issues uniforms that are "hunter green," and lets them wear their own T-shirts, as long as they're not blue (the color of prison-guard uniforms), black (too hard to see), gray (other officials wear it), or orange (the color worn by the Correctional Emergency Response Team, or riot control).
It should be noted that a number of states in the US do still use prison stripes. Mississippi uses a variety of colored stripes and as you can see in these pictures they are also in use in North Carolina and Arizona.