In public protests around the world, governments have taken steps to deny or interefe with protesters' access to the Internet and to cellular service. Such access has been critical in terms of facilitating the organization of public protests against repressive regimes. Cut off the network, and you may prevent or at least weaken the protest. Interference with network access also limits the ability of protesters to transmit information about what is happening on the ground.
I wouldn't call San Francisco's BART, a public transportation agency, a repressive regime. However, the agency recently cut off cell service in the subway system in advance of a planned protest. Protesters had indicated that they would use social networking services to coordinate their protest and to report on the number and location of police.
I tend to agree with Eugene Volokh's conclusion that BART's temporary restriction is constitutional under current First Amendment doctrine. In so-called nonpublic forums, government can restrict speech based on its content so long as the restriction is both viewpoint neutral and reasonable. The restriction here is clearly viewpoint-neutral. But is it reasonable? Arguably so, since a significant protest might have interfered with BART service and disrupted travel in the system. Under current public forum doctrine, that's probably sufficient to uphold the restriction.
But where does that logic lead? Might it result in similar restrictions being upheld in public areas that are designated for speech activity? Is the service interruption really so different from barricades, fences, and other physical restrictions that limit or in some cases prevent effective communication? All of these things interfere with, but do not entirely prevent, public speech. A service interruption makes it more difficult to organize a protest. But so do police surveillance, protest zones, permit applications, etc. Perhaps, as Volokh suggests, the distinction lies in the content-based nature of the service interruption. That was clear in the BART case; but it might not be conceded in others. Or is a service interruption a presumptively unconstitutional prior restraint on speech? Courts may ultimately have to address this issue, as authorities seek new means of regulating protests in networked public places.