Some US citizens absolutely hate the US military.
Other citizens respect and value it.
Unfortunately, many of the former group are also dedicated liberals, and many of the latter group are also dedicated conservatives. Given the state of the culture war in the US today, its difficult to determine how much of any individual's opinion on Project Maven is driven by their opinions as an individual, and how much is driven by their allegiance to one their side in the culture war.
It doesn't help that the political right has made veneration of military service one of their core principles. The left's claim is that veneration of military service is used as a psychological wedge to lever support for military action as well, and they are probably right (for some fraction of the population).