The usual progressive critiques of libertarians on a few points pop up. For instance, supposedly a bunch of white men don't care about abortion rights for women. Now of course, men actually have more favorable views toward abortion than women do, so I'm not sure how that opinion is reached firstly. More importantly I think there's a split within libertarian camps on how to deal with this issue. I think the other side of that split is wrong (that is: a fetus is a human being, life begins at conception, therefore, abortion should be illegal, with maybe some exceptions. Even if you accept the first two premises, it's not clear that the conclusion follows), but there is at least a legitimate debate within libertarian circles on how to handle this. A debate which is little different from that of the general population. Paul ends up with a rather more extreme position on this than he does on many issues. That is troubling to someone like me, and presumably to progressives generally. What confuses me is what they think someone like him could do about it if elected. He could re-institute the Mexico City resolution... and that's really about it. I suppose he could try to nominate some explicitly anti-Roe/Wade judges to the Supreme Court. But Democratic Senators could easily block such a nomination if it alters the Roe-Wade balance. Realistically there's a whole host of other pro-Paul positions on which progressives (and conservatives for that matter) would probably find his judges to be more disconcerting. Paul's position on abortion is basically boilerplate social conservativism, and more or less what you'd expect from a GOP candidate (with the possible exceptions of Johnson, and maybe, maybe Romney or Huntsman). His position on something like the right of contracts relating to the 14th amendment is likely to be a little more annoying given that it strips out a ton of government regulation on a federal level especially, perhaps state or even local level. But this doesn't come up as often.
Secondly. Speaking now of Paulite supporters rather than Paul himself (somewhat). There's a real impetus behind some elements of neoisolationist strands of thought in this country that has more to do with ostrich in the sand sort of thinking. "Who cares what happens over there?, it's OVER THERE!" They'd say. This is foolish. Even if you tend toward a generally more hands off foreign policy (a realist might also do this, by noting the waste of national resources on non-essential foreign entanglements), it is silly to completely ignore the outside world and pretend it can go away. Paul has a version of this in his rhetoric and it is more noticeable in his overall platform, where it stresses disengagement with multilateral diplomatic institutions (NATO, WTO, UN, etc), strong anti-immigration protections, and general opposition or disinterest to free trade. The stronger version of this carried out by some of his political support is populist protectionism, mercantilism, industrial policy (which Paul may or may not support), and ultimately a general attempt to dismantle the institutions of free trade and mutual support throughout the world. I don't think that's going to happen anytime soon, no matter how unpopular the UN and other such institutions are. And of course, I see there are tremendous economic and cultural benefits from immigration and trade that such attitudes are explicitly writing off in a foolish attempt to recapture some sort of 1880s or maybe 1950s mentality of America. I like Ike (or Grant and/or Cleveland) too, but there's a whole bunch of stuff that went down in the 50s that I'd want no part of (McCarthyism, trade barriers, top-down regulations, segregation, etc). The 1880s aren't much better on these matters. And a lot of that sort of cultural phenomenon came from these same attitudes (xenophobia, racism, fear of others, etc). Sorry, but as fun as nostalgia must be (I have no nostalgia for the 80s or 90s myself, and certainly none for this last decade), you're going to have just exercise it in your own head and not carry it into political messages. Reminisce. That world is gone. The new world has integrated with the old. It's no longer acceptable to ignore billions of people and presume that their activities can and will have no impact on your life. That's not the way things work. It might be sensible to learn about these people and their activities, and it might be sensible to ask what you or others you can encourage can do in response (to say earthquakes in Pakistan or Japan or famines in Africa, etc), rather than to ask what US military might or maybe even foreign aid can do first. It is not sensible to live ostrich style. Everything now is connected and the world is "flat". So to speak. China or the Middle East aren't just "over there". They're right here too.
On this matter, I can see a lot that anyone should fear a Paul-presidency or nomination.