u/Pitisukhaisbest

1. Romantic rejection - the singer is rejecting a suitor.
2. Autobiographical - Dylan is rejecting the "prophet" image people put on him.
3. Protest - the "babe" is the US government at the beginning of the Vietnam War, or in general any government wanting its people to fight: "Someone to close his eyes for you /Someone to close his heart /Someone who will die for you an’ more" - he doesn't want to close his eyes to atrocities and kill and die.

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What's so clever is 2 and 3 are opposites, it can be read as Dylan telling us he's unable to live up to our projections of him and him being a protest leader.