Especially as Republicans the country over try their hardest to make important parts of what he advocated for difficult, against policy, it even completely illegal. He's the one who coined the term "affirmative action" and you should definitely look into what he meant and why he said it.
People who hated Dr King raised kids and grandkids who hate Colin Kaepernick and Black Lives Matter and critical race theory, regularly argue that Black culture is pathological, weep and gnash their teeth about reverse racism, and believe that the demographic decline of a white American majority will ruin the nation.
People who thought he was a disgusting and immoral person and that his influence on American culture was poison and cheered when he died raised kids and grandkids who support Trump.
Increasingly, your average conservative is no longer a person who thinks that we've moved past hardcore racism and that the problem of racism is simply being exaggerated by minorities and opportunistic progressive politicians. These days your average conservative is somebody who actually believes in racism and believes that it is a significant problem in the country, but genuinely believes that the only malignant form of racism that exists right now is against white people.
People who despised Dr King raised children and grandchildren who now think this way and vote this way. I'll bet you all the money in my savings account against all the money in yours that Donald Trump's father used the n-word to refer to Dr King a thousand times in front of his son.
Every single politically literate person in the country knows that if a recording emerged of Donald Trump using the n-word to refer to Barack Obama, not only would it not hurt his chances of becoming the Republican nominee and even becoming president, but it would almost certainly help his chances.