Right, but this correlation with "blueness" is, I think, accidental and doesn't account for small businesses.
For example, I would expect more small local businesses in red states than blue states. The tech sector will favor large corporations because of the magnitude of investment involved, at least traditionally (if we are to believe the "economies of scale" explanation; some challenge it, but at the very least, it is causally relevant). So you might see more startup entrepreneurship in blue states because that's where the tech expertise is already concentrated. And because those in tech tend to have college degrees at higher rates, and colleges tend to encourage neoliberal and left-leaning views, you should expect to see more tech in blue states because of that, so you have a self-reinforcing process (there are of course other considerations).
But I wouldn't attribute entrepreneurship to the presence of social programs. On the one hand, those who need social programs are not going to be very educated and are most likely going to be much more interested in making basic ends meet over some business venture. On the other hand, once they receive social benefits, they are often not very motivated to try to start a small local business like a food cart either since they have food on the table. So you need to appeal to cultural factors to account for motivation as well.