This wrongly assumes Americans are not warmongers at heart. A majority of Americans love the idea of bombing enemies and love the military.
Rand Paul will get outright booed at GOP debates during foreign policy questions.
Paul actually seems pretty skilled at using emphasis and packaging heretical ideas to make them more salable to GOP rank and file. But it's still not enough and, like anyone who wants to win, he'll flip and water down his views as much as he needs to to make it through a primary. He's already been doing this plenty. Then, if by some freakish stroke of luck, he won the nomination, his differences with Hillary on foreign policy would be muted. And people don't vote on that anyway, as others point out, but it would affect elite opinion and you'd have Rudy Giuliani and Elizabeth Warren sitting next to each other on Hillary's campaign bus.