At any given moment in this country, there are museums, galleries, performing arts centers, film societies, theater groups and book clubs, all focusing on the artistic work of people who share something in common: race, gender, religion, sexual identity. And the assumption is almost always the same: that people who are demographically alike in some way must produce artworks with something in common.

“30 Americans,” an exhibition of art by African Americans at the Corcoran Gallery of Art, is another such exhibition, and it necessarily shares the ideological confusion of most of the others. Drawn from the extensive private holdings of the Rubell Family Collection, “30 Americans” is a smaller version of a show first mounted at the Rubells’ home/museum/art center in Miami in late 2008 and early 2009. The title, identifying the 31 artists represented as simply 30 Americans, cleverly hints at the inevitable confusion contained therein: Do the artists belong to a coherent group, is it a group that can be identified by race or skin color, and is this a liberating, restricting, or simply an ineluctable category?

The exhibition arrives at the Corcoran slightly more than 18 months after the museum announced that it had sold the Randall School, a property in Southwest Washington, to a partnership that includes Don and Mera Rubell, who have announced plans to redevelop the property as a museum and hotel complex. So there are two problems that haunt this show — its premise is problematic, and it has the appearance, at least, of being a conflict of interest.

The first problem is substantial indeed, but at least it has been addressed. Almost every work on display is in some ways an argument with the basic organizing principle of the exhibition. Far from being simple exemplars of African American art, the works in “30 Americans” range from parodies of that idea to direct confrontations with efforts to categorize, define and contain racial identity.

Two of the most visually sumptuous, Kara Walker’s 1998 silhouette mural “Camptown Ladies” and Kehinde Wiley’s large-scale 2008 oil painting “Sleep,” limn many of the basic strategies. Walker’s paper cutouts depict stereotyped African American figures, still dressed as if in the South of slavery or Reconstruction, dancing across a white wall in strange orgies of eroticism and violence. Unlike artists of earlier generations, who sought dignified portrayals of African American life and fought to redeem categories of racial identity, Walker embraces the worst of it, sets it in motion, makes it beautiful and invites the spectator to be seduced, entertained and ultimately horrified at the spectacle. There is an implicit hope that these minstrel figures will dance themselves to death, setting to rest an invention of white racism.

Wiley’s baroque paintings, in which contemporary African American men are interpolated into sumptuously detailed and meticulously painted canvasses that make reference to some of the most theatrical paintings in the Western “white” canon, suggest a willingness to surf above the complicated history of racial identity, parodying, borrowing and subverting at will.

Walker, Wiley and some of the younger artists in the exhibition have sometimes been lumped together, as representing a latter-day refusal to participate in an aesthetic that takes “black” for granted, as a meaningful, coherent, celebratory category. They come after all that, after the Black Arts Movement of the 1960s and ’70s, with its themes of solidarity and pride. They are analyzing, enacting and playing games with ideas about race they have found in the world, rather than attempting to live out through art some dubious, idealized notion of race.

The exhibition reaches back to artistic figures who are now considered canonical elders among many African American artists, including Robert Colescott and Jean-Michel Basquiat. The diversity of art on display necessitated some kind of organizing principle, and the curators of the Corcoran show have used these elder figures (Basquiat died at age 27, but that was more than 20 years ago) to anchor different rooms with broad general themes, such as storytelling, or urban identity. These connections are not readily apparent from the work itself, nor is the complicated intellectual history (explored in the catalog) of how race has been conceptualized over the past century or more.

And so you have two choices at the exhibition. One involves forcing the art to represent or illustrate something else, the intellectual construct of race, in which African Americans have attempted to retain their individuality while participating in or resisting a collective identity that they may or may not feel is their own invention. If you follow this path, every work seems to be about speaking in two or more voices, wearing masks or unveiling the self, creating private meanings that resist the outside world, or mixing up visual and racial ideas into your own perfect elixir of identity.

The other is to set aside that history, with its convoluted twists and turns, its manic refusals to be black or futile efforts to redefine what black means, its courageous acceptance or defiant resistance to social determinism, and simply enjoy the work as art. And if you follow this path, the exhibition seems like a wild scrapbook of unrelated and discordant visual material.

Neither is satisfying, nor fair to the artists involved. You sense from most of the artists that they are keenly aware of the paradox, that they know full well how much the art world participates in the same efforts to categorize, reduce, brand and market racial identity as the world at large. In the end, the work that matters, that survives the complicated game of making an exhibition about race when everyone acknowledges that there is no agreement about what race means, or should mean, is the work that resists to the very end, that refuses to participate, that bears some final trace of something elementally human, whatever that means.

Rodney McMillian’s “Untitled, 2005” is a large, once-white carpet, hung on the wall. It is filthy, stained, discolored and worn. A white rug is a statement of aspiration, to an orderly, elegant life. A soiled white rug is like a piece of film, though even more sensitive, recording the direct impress of time, poverty and despair. McMillian’s “Untitled” is a powerful standout and an exception to the many more technically crafted and visually brilliant works in the exhibition. It is simple, poetic and haunting, and it allows the artist and the people who made the art — the people who soiled the rug — to disappear while leaving traces more evocative than many representational paintings.

And that raises the issue of the second problem with “30 Americans,” the appearance of a conflict of interest in presenting a private collection at a prominent museum, especially when a financial transaction has happened between the parties. Is this a quid pro quo between the Corcoran and the Rubells that serves to boost the value of a private collection?

The Rubells have categorically denied any quid pro quo, and Kristin Guiter, spokeswoman for the Corcoran, says “the two are completely unrelated.” Discussion of the “30 Americans” show began well before any plans to sell the Randall School, she says.

A few things militate against a cynical view of the question. First, the work on display is important and needs to be seen. Second, the Rubells probably bring more prestige to the relationship than the Corcoran, which has been damaged by financial and institutional mismanagement over the past decade. Third, museums would hardly exist without courting the favor of private collectors.

But McMillian’s “Untitled” demonstrates why one should never be blasé about even the appearance of a conflict of interest in the museum world. It is, after all, just a rug. Its status as art depends entirely upon a social convention: that it circulates in the art world as art. That’s a frustrating way to define art, but it’s the only one we have. When people who study art, collect art, preserve art and present art agree that something is art, by definition it becomes art.

Collectors are one part of this equation. But a more important, substantial and essential part of the equation is the intellectual apparatus of the art world, the critical and curatorial function, which has no vested interest in whether it’s just a rug, or a work of art that uses a rug as material.

If there’s a danger between the too-close relationship of museums and collectors, it is at this far horizon of the art world, where people legitimately wonder, is it really art? Does it really say something? Those are essential questions, which any intelligent person will feel standing before a work such as McMillian’s “Untitled.”

A respectable museum has the intellectual authority to ask its visitors to do something remarkable, dangerous and thrilling: Accept a soiled rug as art. If you can do that, there is an enormous reward. McMillian’s rug breaks through the intellectual torment of “30 Americans,” the sense that so many artists are in flight from something they never asked to be. It reminds us that the greatest art is never about the value of the object, but rather, its power to force feelings to the surface, evoke acts of empathy, engage currents of thought.

It’s a lot to ask of people, to accept a rug as art. Which is why the curatorial authority of a museum should never be compromised, even by the appearance of having perhaps too close a relationship with collectors.

30 Americans

at the Corcoran Gallery of Art through February 2012. For information about hours, location and admission, visit www.corcorcan.org.