Themes of Get Out

I think the primary theme is of black bodies being exploited for the benefit of elite whites, while black minds are controlled and co-opted. The "sunken place" is specifically used as a metaphor for the suppression of black identity in a white-dominated culture. This theme has obvious connections to the American practice of slavery through the mid-19th century; to the problems black people face in their interactions with white-dominated authority; and to the problems faced by black cultural expression in a white-dominated culture.

A secondary theme is that many whites who express a belief in racial equality still support institutions and policies that express racist thought.

Jordan Peele spoke to Deadline Hollywood about the film, and specifically mentioned wanting to subvert the white savior trope:

Peele cites Kevin Costner in Hidden Figures and Brad Pitt in 12 Years A Slave ... he points out that the role of those characters is to speak to white audience members saying, “Hey! This is you!” as a form of reassurance to remind them that they aren’t racist. With the character of Rose (Allison Williams), the audience expects to see her come out as the white savior to save Chris, but Peele made a bold move to not have that happen. He points out that there is this trend in race-driven movies where the last good white person can’t be racist, like Costner and Pitt. “Rose subverts that,” said Peele.

Brandon Harris, writing for The New Yorker, points out that,

The film ... brazenly inhabits the anxieties that surround miscegenation [romance between black and white people] in our still racially stratified country.

Harris quotes Peele as saying:

...there was a time when I went to a girl’s parents’ house for the first time, and I was nervous because she hadn’t told them I was black.

Later in the same review, Harris quotes a response from Peele during a Q&A regarding the movie:

The real thing at hand here is slavery...

Vulture.com quotes Peele talking about his take on the 2008 primary race between Hillary Clinton and Barack Obama as partly being about racism versus sexism, which was part of the inspiration for the film:

I had never seen the uncomfortableness of being the only black guy in a room played in a film. That notion is a perfect state for a protagonist of a horror film to be in, to question his own sanity. Rosemary’s Baby and The Stepford Wives were movies that did with gender what I wanted to do with race.

In the same interview, Bradley Whitford talks about the ending:

The ending he ended up with does a brilliant thing, because when Chris is strangling Rose in the driveway, you see the red police lights, and then you see the door open and it says “Airport” and it’s a huge laugh, and everybody has that same laugh and release. You understand from Chris’s POV that if the cops come, he’s a dead man. That is absolutely brilliant, non-lecturing storytelling.

And a student taken a class on the movie is quoted as saying,

Peele told my class that when he was writing the scene with the sunken place, he realized that it represented the prison-­industrial system.

There are a lot of themes to unpack in Get Out. I'm sure I could keep doing web searches and quoting Peele from various interviews and we would likely see him talk about every aspect of racism and how it is portrayed in the film. Here's a summary of the themes mentioned above:

• The White Savior Trope: The movie is written and cast to make it seem like in the end, Rose is going to be the one good white person who will save Chris, but she is actually as evil as her family and their friends, and she ends up being the last white person that Chris has to escape from at the very end.
• Anxieties About Miscegenation (with a side of white privilege): Chris is borderline panicked about the fact that Rose hasn't told her family that he's black, because he knows that white parents can be very uncomfortable about that. Rose shows her privilege by thinking it's not a big deal (although we later learn that the family knows that she will be bringing another black man home for their evil schemes).
• Modern Slavery: In the film, black people are enslaved by white people in a horrific way, and also a way that isn't obvious. Another recent film, 13th, is a documentary suggesting that the incarceration of blacks in America is a way to perpetuate slavery in disguise.
• The Societal Horror: Chris spends the entire movie surrounded by white people, all of whom we later learn are evil and are attempting to enslave his body. Even the black people Chris meets are already enslaved and are also evil inside. He feels uncomfortable, isn't sure why, and no one empathizes with him about his discomfort. This highlights how black people can feel on a daily basis in a society dominated (numerically and culturally) by white people.
• Racial Profiling and the Assumption Of Guilt of Non-Whites: When the police car pulls up at the very end, the audience is meant to think that Chris is doomed. If the cop in the car doesn't shoot Chris dead, no one will believe his story and he will be jailed for multiple murders. And in the end, it will be because he is black. Even though the reveal that the police car is driven by Chris' friend there to save him, that reversal of fortune serves to highlight the implication that immediately precedes it.
• The Prison-Industrial System/Complex: This connects with the theme of modern slavery, above. An aspect of this not discussed above is the financial incentive of privately owned prisons to have more inmates, which drives lobbying for tougher laws (e.g., "three strikes" laws). Racially biased enforcement and prosecution creates an industry of incarcerating black people for profit, and the metaphor for this in Get Out should be clear.