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I don't want arguments for or against the wall/barrier on the United States' southern border. I would like to understand what Nancy Pelosi means when she or any other member of the Democratic party claim that a wall is immoral.

Here are some examples of statements by Democratic politicians and my best guess at interpretation:

Speaker of the House Nancy Pelosi called President Trump's planned border wall 'immoral'

“A wall, in my view, is an immorality. It’s the least effective way to protect the border and the most costly. I can’t think of any reason why anyone would think it’s a good idea — unless this has something to do with something else.”
Source

What Speaker Pelosi seems to be saying here is that the border wall is immoral because it's costly but it's not even effective, and would therefore be immoral waste of taxpayer money.

Congresswoman Alexandria Ocasio-Cortez stated that all Latinos wherever they're from have the right to enter the United States, so in her view, not letting them enter could be perceived as a violation of their rights, which could be considered immoral.

Rep. Adam Smith, the new chair of the House Armed Services Committee, who, echoing many other Democrats, claims that Trump’s campaign for a border wall is rooted in “xenophobia and racism.”
Source

So in Rep. Adam Smith's view, if the border wall is rooted in 'xenophobia and racism', then the border wall is immoral because xenophobia and racism are immoral.

Rep. Veronica Escobar, D-Texas, stated

“I hope folks have realized walls are deadly,” she said. “When people are so desperate they will flee their country to go to another, a wall doesn’t stop them. It just pushes them out to more treacherous, dangerous, deadly crossings where migrants die in the desert or drown in rivers.”
Source

So, in Rep. Escobar's view, the wall would be immoral because it would make migrants' journeys more dangerous and expose them to potentially greater harm that if there weren't a wall.

In terms of cultural references, it is worth mentioning a powerful image dating from the Cold War: the fence that separated Europe in two (and surrounded West Berlin) during the Cold War was called "the Wall of Shame". Its numerous photographs were the symbol of the totalitarian oppression of the Soviet Union. It was also transcontinental, since it went uninterruptedly "from Stettin in the Baltic to Trieste in the Adriatic", in the words of Winston Churchill (5 March 1946).

It had a strong impact on European mentalities, but on the US culture as well. US President Ronald Reagan famously stated "Mr. Gorbachev, if you love peace... open this gate! (...) Mr. Gorbachev, tear down this wall!" (June 7, 1987).

Philosophically, there is a duality in walls, especially when they go from coast to coast: even though they are purportedly built to protect the people on this site from contamination (the German Inner Wall was justified as an "anti-fascist protective rampart"), they are often meant the other way: "to keep the other people in"; in other words, to keep people as prisoners.

Furthemore, let us not forget that in US cities, actual walls or bureaucratic walls were built to segregate black populations from white ones, in the fear of an "invasion" of "people bringing drugs and crime" (Chicago's housing system left a strong memory of this; see also N.Y. Times's book review, 20 June 2017). That explains why the N.Y Times used the term "wall of shame" (24 January 2019) about issues of racial discrimination:

The wall of Donald Trump’s campaign and presidency has always operated
both as a discrete proposal — an actual structure to be built under
his leadership — and as a symbol with a clear meaning. Whether praised
by its supporters or condemned by its opponents, the wall is a
stand-in for the larger promise of broad racial (and religious)
exclusion and domination.
It’s no surprise, then, that some Americans use “Build the wall” as a
racist chant, much like the way they invoke the president’s name. And
it’s also why, despite the pain and distress of the extended
government shutdown, Democrats are right to resist any deal with the
White House that includes funding for its construction.

The term wall of shame has two connotations here: the first as a metaphor for immorality, the second as a reference to the Berlin Wall.

Hence, in the US, the question of the Mexican Border Wall does evoke two images, both of which are profoundly immoral in modern US culture: the Iron Curtain across Europe as tool of political oppression, and racial segregation in the planning of US cities (and these two images were already connected in the first place).

To moderator

This post uses abundant references. Please be more specific/helpful, to avoid your moderation being considered as overzealous.

The 2016 Democratic platform says

The world is experiencing a major refugee crisis with more than 60 million people displaced as a result of conflicts in the Middle East, Africa, and Eastern Europe. We support President Obama’s call for an international summit to address this crisis so that every country assumes its responsibility to meet this humanitarian challenge. While Donald Trump proposes banning Muslim refugees, we will look for ways to help innocent people who are fleeing persecution while ensuring rigorous screening and vetting.

They also write

Democrats know the importance of our country’s history as a nation of immigrants. We honor our fundamental values by treating all people who come to the United States with dignity and respect [...]

Democrats with some Republicans passed the Refugee Relief Act of 1953 in reaction to the end of WWII and the start of the Cold War.
They did agree with most civilized nations that people who faced genuine political persecution deserved political asylum, and that there should be individual hearings in a legal process.

Asylum should happen in the first safe harbor after leaving the place of persecution. There is no right for the refugee to pick their destination. The problem with that is that most wealthy nations, those most able to cope with refugees, have declared their immediate neighbours as "safe" and tried to prevent asylum claims by other ways -- migrants have to get in illegally to get a hearing if they will get legal refugee status.

So you can see Democrats supporting some restrictions on refugees, while generally being more welcoming than Republicans.