While acknowledging that branding someone a racist or bigot is a serious charge, Trump has made some regretful choices that have led to this charge. Of course, it's not definitive and people can feel free to challenge this designation.
First, here's my definition of racism:
a belief that one race is superior to another based on intelligence, physical prowess, or culture. Prone to being overly reliant in describing a racial group on negative stereotypes.
For brevity's sake, here's a source from Fortune magazine, which is not universally considered a liberal media source:
http://fortune.com/2016/06/07/donald-trump-racism-quotes/
Point 1: Has already been convicted of racial discrimination where he was charged with denying blacks access to their rental property. The investigation took place under GOP president Richard Nixon and was supported by testimony from Trump employees who said he screened applications by race. This case was eventually settled and Trump was forced to comply with additional regulations.
Point 2: Made a naive statement about blacks having an advantage over whites due to affirmative action. While many whites feel that's the case, it's intellectually dishonest to say that Trump would have been better off if he was black. For one, in the 1980s, differences in wealth between blacks and whites was immense, with some of that attributed to blacks facing significant obstacles in purchasing private property across generations. Would Trump have made it without his father's success? This is questionable.
https://www.youtube.com/watch?v=7K4I2j39-jU
Point 3: Former Trump executive John O'Donnell claims to attribute this racist quote to Trump, "Black guys counting my money! I hate it. The only kind of people I want counting my money are short guys wearing yarmulkes… Those are the only kind of people I want counting my money. Nobody else…Besides that, I tell you something else. I think that’s guy’s lazy. And it’s probably not his fault because laziness is a trait in blacks.” Whether Trump said it is not definitive, though he admitted that he probably said it in a Playboy interview.
Point 4: Can't name one prominent black executive in the Trump Organization. While certainly not proof of racism, it certainly runs counter to his claim of being the 'least racist person on earth'. Given that a large number of Fortune 500 companies have at least one minority on their senior executive team, that's difficult to fathom that he couldn't find one over his long stint in business.
Point 5: Said that Curiel couldn't be fair because he's Hispanic. While recognizing that Hispanic is an ethnic group and not racial, there's little difference from being called a bigot rather than a racist. Given this rationale, is he saying that white judges can't be fair when there are black defendants who have said incendiary comments about whites?
There's my case. Now the question is can other dispute these points with reasoned comments. I doubt it, but prove me wrong.