That said, libertarians like Paul would have been against funding the projects that led to the Internet, and are today against funding similar government projects that might lead to future innovations.
In many cases, innovations are bootstrapped by government funding or research, and then handed off to an appropriate role by the free market. Libertarians are usually against regulating the private market once the handoff has occurred (for good in many cases, and definitely in this case), but they are usually against the initial government bootstrapping.
It's easy to imagine attacking the initial ARPA work on privacy, anti-military, or anti-elitism grounds, and I could easily imagine it losing its funding today, decried as a boondoggle that was useless for regular Americans, who of course would never have access to a computer, with taxpayers footing the bill.