It is legal to photograph a military base (or any other government property, for that matter) in the US, provided that you do it from the public right-of-way (or any other place you would otherwise have a right to be). Unfortunately, MPs, sheriff's deputies, and municipal police officers (if applicable) are very likely to hassle you about it anyway, and possibly also detain you on any convenient pretext, should you attempt it.
This had bred a variety of protester that will stand on the public sidewalk, photographing things, until a cop shows up. The police encounter is recorded in its entirety. Depending on what the cop does, the protester may then sue for rights violations, and typically receives a settlement offer after the judge sees the video, which then gets posted to the Internet to fan your outrage.
I may have misread your tone, but you sound as if you find such protesters distasteful. I for one hope they bravely continue, until such time as one need not fear being detained on convenient pretexts for legal activities.
Yes, you definitely misread. The only thing I find distasteful about such protests is that those cops who enforce laws that do not exist are not generally held personally accountable for their actions in any meaningful way, even when they cost their county/municipality tens of thousands of dollars for just a few minutes worth of unprofessional conduct.
This had bred a variety of protester that will stand on the public sidewalk, photographing things, until a cop shows up. The police encounter is recorded in its entirety. Depending on what the cop does, the protester may then sue for rights violations, and typically receives a settlement offer after the judge sees the video, which then gets posted to the Internet to fan your outrage.