What does this phrase mean: "they just can't keep their hands off the cookie jar"?

Sounds kinda racist to me. Your use of the terms racism, black people, discriminated, lack of opportunities, and bias, leads me to believe that the cookie-jar metaphor is all about a relatively common "white" attitude about Blacks in America today.

I think what is implied in the statement you highlighted is that Blacks get so frustrated with the lack of genuine opportunities to get ahead (and thus better themselves) that they kind of give up and resort to reaching into the government's "cookie jar" of welfare benefits and government programs.

These governmental benefits and programs can sometimes be just short-term solutions to complicated and deeply entrenched social problems. Systemic racism is one of those problems. Citizens (especially non-minorities) who have it "made in the shade," so to speak, look down on people who "work the system" in order to get their cookies instead of "working hard in the system" to earn their success. They're the kinds of folks who are quick to say to minorities

Hey, just do what I did. Get a good education, get an entry-level job, keep your nose to the grindstone (i.e., work really hard) and almost before you know it you'll be working your way up the ladder of success just as I did!

What those folks fail to realize is that "the system" does not work the same for minorities as it does for majorities. Minorities often find themselves in a Catch-22. A Catch-22 is a situation in which a person is frustrated by a paradoxical rule or set of circumstances that preclude any attempt to escape from them. Any move that a person can make will lead to trouble.

In this case, a minority who reaches into the cookie jar (something the non-minority will call the "easy way out") is criticized for being lazy and not wanting to better himself. On the other hand, a minority who attempts to buck the system which is rigged against him is labelled a "troublemaker." He is accused of somehow trying to subvert the system by "forcing" it to do things his way. In reality, all he is doing is attempting to create a "level playing field" for all people, himself included.

Neither behavior is without its own set of problems, and both behaviors engender no small amount of cognitive dissonance for the minority. The old saying, "Damned if you do, and damned if you don't" is perhaps an apt expression for this phenomenon.

The cookie jar is where all the goodies are, and you're only allowed to remove a cookie if Mom says so. The most familiar idiom associated with it is "caught with his hand in the cookie jar", meaning someone was helping himself to money from petty cash accounts or something of that nature and got caught.

"Cookie jar" is also sometimes used to refer to sexual relations, especially with underage individuals. You can kind of understand the implication -- the jar is to be kept closed, but someone sneaks it open.

As generally understood there are no racial overtones to "cookie jar", though certainly there may be segments of society which have assigned some sort of racial significance to it.