Is Trump racist for building a wall?
A: It could be, depending on your motives. If your motive is that you think all latinos are inferior to whites, and that's why you want to keep them out, then it could be racism. When FDR started it, or Bill/Hillary Clinton's campaigned on it (calling it a fence), or Obama demanded better border security, the Democrats didn't call it racism. In order to show it is racism, you'd need to show that Mexicans are a race, and that Trump doesn't like the entire Mexican people. But racists don't usually hire, hug Mexican voters, and celebrate lowering latino unemployment. Anyone who cares, knows that Trump is fine with legal immigrants (though probably less so than I am), just not illegal immigration. So unless you have evidence against the more likely scenarios, assuming the worst shows the bigotry of the accuser more than the accused. But that won't stop/slow the media left from doing it.
The Mexico-American border is the most heavily crossed border in the world, both legally and illegally. The history of "the wall" or fence goes like this:
- 1937 under FDR with the Organ Pipe National Park (ORPI) building cattle fences to prevent Mexican cattle from overgrazing on American land
- 1951 President’s Commission on Migratory Labor to address the "Wetback" problem. It can be summed up that during WWII, instead of recruiting American workers from Hawaii, Puerto Rico and other places that needed work, Democrats created a program to recruit from Mexico and teaching them to come up here and work and send their money home. A few years later, we had half a million illegal aliens, and the mess had been created. They did a study on the problem and what to do about it -- and recommended all sorts of things, but Democrats refused to implement those suggestions. 
- 1960's and the "War on Drugs" started the creation of a barrier in earnest, and was expanded under Nixon in the early 1970's.
- 1986 Immigration Reform and Control Act (IRCA or Simpson–Mazzoli Bill) responded to rising illegal immigration problem by providing one-time-amnesty for 350,000 illegal immigrants (to offset fears of a lack of farm workers if there was an immediate crackdown), in return for increased border security (the promise of the fence by Democrats), decreasing illegal immigration, and penalties for companies "knowingly" hiring illegal immigrants. A couple decades later, Democrats had repeatedly broken their promise to help secure the border (and obstructed it), illegal immigration had over doubled, Simpson and Mazzoli both admitted regrets for it's failures (caused by Democrats undermining it), and and the 350K amnesty was actually 3 Million (about 1/6th of the adult male population of rural Mexico, using phony documents), and is called the greatest immigration fraud in American history. It showed what happens when you trust Democrats.
- 1994 NAFTA harmed Mexico previously protectionist agriculture with cheaper American produce, this (along with a booming dot-com economy) caused a big immigration wave north, and increased the pressure on better immigration controls.
- 1996 Bill Clinton's State of the Union address promises, "One of these areas is the problem of illegal immigration. After years of neglect, this administration has taken a strong stand to stiffen the protection of our borders." to finally live up to to the promises of 1986
- 2003 Israel's first major segment of the West Bank barrier is completed (this was started in 1992), the effect is an immediate reduction in violence and suicide bombings. Each new segment sees further decreases, and this invigorates American politicians aware of the problem, to follow Israel's lead. Are they all racists? 
- 2006, After 9/11 Congress authorized the Secure Fence Act, under the guise of national security: a multi-billion dollar plan to build hundreds of miles of fencing along the border. Hillary Clinton speaks out in favor of the wall. She tried to walk that back after the Trump issue by claiming she was "for a fence, but against a wall", completely Clinton'ing the topic. Yeah, a fence is less racist than a wall.
- 2007 After the 2006 election brought them wins, the Democrats start walking back their promises, delay many parts of the project, start pushing for more "environmental studies", and by 2010 put a freeze on the project, due to cost overruns partly caused by their shifting requirements, delays and studies. Inn the end while $50B was allowed, the Democrats were able to make sure the $2B that eventually got to border security was wholly ineffective -- causing the fight we have today. 
- 2014 ISIS and Al Queda are sending people to Mexico with the intent of them crossing the border and infiltrating the U.S. illegally. A few are caught in the U.S., but in immigrations usual catch and release program, they are released in U.S. before identified, and they disappeared.
- 2019.01.09 Obama's Border Patrol Chief: Democrats talk of a "manufactured" crisis misleads the public -- the crisis is NOT manufactured. 127 agents have died defending the border. 
Reagan - We have a border crisis
Where we sit today is 580 miles of the 1,954-mile border with Mexico has some sort of official fence. (There are other tracts which may have something like cattle fencing / barbed wire, but are local ranchers fences, not official border control). Around 400 people die per year trying to cross the border illegally, but it fluctuates dramatically depending on the economy. There are a few overlapping issues : immigration laws, national security, and broken promises.
Republicans feel the Democrats have been promising then obstructing their side of the agreement -- because Democrats win key votes with the help of illegal aliens (lookup my old haunt, the 46th district and Bob Dornan / Loretta Sanchez as an example), and Democrats see it as a wedge issue where they can play both sides. They tell the Unions and Americans they'll fix it, tell latino's they're against it, and calls anyone that tries to fulfill their promises a racist. It's win-win for them.
Progress is harder because of past broken promises by the Democrats, and their demagoguing. This is like when the Democrats torpedo'ing Bush's immigration reform by calling it amnesty, (turning his party against it), while selling the Latinos that the failure was all because of the Republicans. Or like Obama's unconstitutional executive overreach (he's been ruled against many times by federal judges and Supreme Court), or lies that ACA wouldn't cover illegal aliens (but does), that causes political backlash against amnesty and illegal aliens, then they use that backlash to paint the Republicans as racist, for this political fight.
But if the wall / border fence is racist, then all the Democrats that supported it, including Hillary Clinton, are racists as well. No one should get it both ways: to get to accuse the other side of being evil for doing what their side advocated as well.