Why did the Tethered form a line in Us?

They were recreating the Hands Across America event that the woman remembered from the TV ads when she was a child. That’s why they were wearing red, because in the art for the campaign, it used red cutout figures to represent the people spanning the country.

It’s not as clear why she’s obsessed with hands across America but my read is that she didn’t fully understand or remember what happened to her, she just had these strange dream like memories of a happier time, and that was a big one of those memories. Also it seems like the Tethered aren’t able to think or organize or talk, but she can. So the hands across America event is a concept she can use to organize and motivate them to go to the surface.

Finally there’s the symbolism (out of universe). The title “Us” seems to also meant to be read as “U.S.”, as in “United Stares”, and the movie as a whole is a comment on race relations in America. In the movie, there is a literal subculture and underclass of people who are never given the education or opportunities they need to better themselves. The Tethered symbolize people of color in America who in reality are oppressed by systemic racism. Just like the real Hands Across America was ineffective at changing outcomes for people, (NYT called it “a superficial gesture that offered no long-term solution to poverty in the United States,”) so is the one in the movie meaningless after the slaughter, and it reinforces the theme of American culture in the movie.

This New York Times excerpt quotes Peele himself on it:

In an interview, Peele said that as he was writing “Us” he stumbled across a commercial for the event and “got this really eerie feeling.” A Hands Across America commercial of the director’s own making plays at the beginning of the film. “There’s something cultlike about the imagery that makes me think of the Manson family singing folk songs as they leave the courtroom,” said Peele, who was 7 when the nationwide gathering happened. “There’s like an insistence that as long as we have each other, we can walk blindly past the ugliness and evil that we may be a part of.”

Esquire has an article about this same question.

Hands Across America was a benefit campaign, sponsored by USA for Africa (the organization that produced the 1985 charity track "We Are the World"), in which people within the continental United States joined hands in a human chain for 15 minutes.

The beginning of the movie (when young Adelaide first meets Red) is set in 1986, so possibly sometime after when Hands Across America happened (or on the Sunday of Memorial Day Weekend, when it actually happened).

While Red doesn't explicitly reference Hands Across America in her monologue, it's clear that the event made a big impression on her in 1986.

It brings new symbolism to Hands Across America, an event originally intended to raise awareness about homelessness and hunger across the world; in the final shot of Us, Jordan Peele reframes the awareness campaign to show that Americans often turn a blind eye to the social ills that exists—quite literally—just below our country's surface.

In the movie there's also a literal division in the US: the people from above and the "shadow people" living below ground. Another metaphor for the economic division that existed at the time.

There's also an article mentioning an interview with Peele on Thrillist:

He told UPROXX that his ideas for Us crystalized when he came across an MTV promo for Hands Across America -- a truly surreal jumble of eyes, fingers and hands -- on YouTube and felt "scared." He decided to open his new film with the younger version of Lupita Nyong'o's character, Adelaide Wilson, as she watches that commercial. "It took me down this path to really think about this movie in terms of this country and the idea of demonstration or protest, or even performance art," Peele said.