tl;dr: Most likely, the white uniform is meant to reflect a prisoner that has just gone through intake, while the orange jumpsuits represent high-security prisoners. This is a not-uncommon practice in US prison systems.

In real US prisons, uniform policy is entirely up to the local or state prison system, but the system presented in Daredevil does have real-world equivalents. It's very similar to the California prison system, with the colors reversed: an orange jumpsuit is given at intake, until the prisoner is classified into a "security" level and given a new color. (Orange is the New Black shows this same system slightly more accurately) So, for example, general population prisoners in California get white or blue clothing, while high-security prisoners may get something more obvious.

Additionally, in many prison systems, different uniform colors may be used for certain categories of prisoner that have different prison access. For example, again in California, prisoners that are allowed to work on or outside the perimeter have green uniforms.

I'm not sure what New York City (where Daredevil is set) prisoners are wearing these days, but I don't think they actually wear orange jumpsuits. Ironically, the success of Orange is the New Black has made the orange jumpsuit "cool", and is causing problems for a lot of prison systems. Many of them are converting back to the old striped uniforms of the late 1800s.

The different colors help the viewer distinguish flashbacks.

I noticed this trick in Tinker Tailor Soldier Spy. I wondered why the film opened with Smiley getting fitted for eyeglasses. That scene didn't serve any purpose to the plot, and it didn't make any sense to include it in the movie, until I realized the movie makes liberal use of flashback scenes, and it is hard to tell which scenes are flashbacks and which occur in the present. Until I observed the glasses. Then I could tell.

Daredevil is doing the same thing with the prison scenes. They clearly wanted to surprise the viewer by withholding Wilson Fisk until mid-season, which meant they had to show the Fisk prison flashbacks at the same time as many of the present-day prison scenes, portraying two parallel time frames in the same location where little changes with time. This would definitely be confusing for the viewer, so the flashback scenes are denoted for the viewer by showing Fisk in white, as opposed to orange, which adeptly removes all confusion.

I guess it's the rule in prisons of Hell's Kitchen to provide newcomers in prison with White clothing. If you remember clips from Season 2- Episode 09 when Wilson fisk is shown remembering his first day in prison after, under arrest, he is also shown to be provided with same white color clothing just like the Punisher.

In the state of Florida, they give white uniforms to prisoners. I would go and visit my grandfather every weekend for 15years. I was told if you have allergy to pollyester, they give you white.

There are no rules for prison uniforms. Each state, each county, each jail can do it differently. In California they don't even have orange--red is for people in the SHU. Sometimes it can be white though. And sometimes red is for classification, or sometimes high-security. It changes constantly. I know that in the feds (I spent 7 years in the BOP) that red means the SHU. It can change for women, however. I guarantee no prison officials are watching the show and changing their colors simply because a show is popular. That matters not one wit to them, unless orange jumpsuits start being stolen---then they would care. In Alaska, for example, they had blue for felons and yellow for misdemeanors, but when a guard in his blue uniform was mistaken for a felon in felon blues, he was shot at. They immediately changed the colors of the prison officials uniforms to a more grey color.

The most accurate element of OitNB, I've noticed, is the red-and-white ID cards you are required to carry anytime you are out of your cell. They are pitch-perfect identical to the ones the BOP issue every inmate.