For example, when Trump says "they're sending", we know he knows that Mexico isn't literally sending these people. They don't pick them up and bus over the border so that they'll become America's problem. Illegal immigrants run the border primarily because the wages in America are so much better than the wages in Mexico, not because someone "sent" them over, except in the metaphorical sense where the country either cannot or does not provide the desired standard of living for its residents, and thus they "send" them away to a place that can and/or does.
Your quote is selectively edited. What is the VERY NEXT sentence after your quote cuts off? "And some, I assume, are good people." How can Trump say they're ALL rapists and then literally in the next sentence say "And some are good people"?
Pretend like you're talking to someone you respect about his position on immigration. Are you going to listen to him say this and take his verbatim statement as his literal meaning, especially when he offers a direct contradiction of that verbatim statement less than one second later? No, you'll do what normal people do, and bridge the gap. You'll know he doesn't think that EVERY Mexican is a rapist. You'll know he meant that a disproportionate quantity of illegal immigrant are criminals of all sorts, including thieves and rapists. You are free to disagree with this all you want, but it's not worth the time to speak to someone who insists on taking the least-charitable possible interpretation. If Trump spoke a bit more quickly and these soundbites were harder to extract, this whole trick would've collapsed a long time ago.
This is really the crux of the matter. Those who are disposed to hate Trump take the crudest possible interpretation, say the surrounding context is irrelevant because it's just trying to throw some ambiguity into the mix so he can pull people off the scent. Those who are disposed to like Trump take the most moderate possible interpretation and look for contextual cues that can exonerate him from the literal meaning, which are available in abundance, because Trump is just a normal guy with an imprecise way of speaking ... ... right?
"Objectivity" is a foreign concept to the human decision apparatus. Humans base decisions almost entirely on the credibility they attribute to the relevant carriers/advocates.
That's why intense hostility is not really justified by either side. The election was really a question of "Which candidate do you feel is more deserving of the benefit of the doubt?", since taken at face value, both candidates were embarrassingly unqualified.
Clinton's campaign strategy was straight up fear-mongering. Legalistically parsing the words of a non-lawyer, stripping context and meaning wherever possible, and using these soundbites to try to frighten minorities into believing that Trump hated them. The American people were not fooled by that strategy, but there are many confused and disgruntled people left in the dust by HRC's divisive methodology. It is now incumbent upon Hillary Clinton to come out and admit that the fears she's planted in the hearts of religious and ethnic minorities are unfounded and were manufactured as a failed political strategy to scare people out of voting for the person they believed could bring them economic prosperity.