Woods has been all over Kaep -- and the NFL -- telling our cameras he's boycotting the league for it's refusal to discipline the 49ers QB over his national anthem protest.
But it's Woods' name-calling of Kaepernick on Twitter -- where he called Kaep a "piece Of S@#t" and a "dirtbag" -- that has Smith steaming mad.
Of course, Smith and fellow sprinter John Carlos are the OG's of the sports protest game ... creating an iconic image at the '68 Olympics in Mexico by raising their fists in the air for Black power.
TMZ Sports spoke with Smith and he told us the personal insults aimed at Colin aren't fair ... and because of them, he can no longer support Woods' movie career.
"James Woods used to be one of my favorite actors ... but if he thinks he is dirt because of what he did then I am crossing him of my list because he is wrong."
Smith went on to say he totally disagrees with Woods' view that Kaerpernick's protest is disrespectful ... and is urging the Academy Award nominee to take a hard look at the issues.
"I think James should look a bit deeper, and focus on the reason [Colin] did what he did."