Several assumptions have been made here.
The most common one is that nearly everyone who enters the military does so to escape poverty. The demographics of today's military don't support this, nor does the journalistic record. Some do join the military to get out of poverty, of course, but there are many other reasons people join. To serve their country, for starters. To challenge themselves. To do something significant in their lives. To straighten their act out. Because they like guns. To continue a family tradition. Because their friends did. Many reasons.
The second assumption is that, without access to certain blogs, military personnel will not be able to come to their own balanced conclusions; the 'brainwashed' theory. It's nothing more than a form of condescension. I can assure you from personal experience that folks in the military are as or more critical in their thinking (after all, their living at the sharp edge of political policy) as the shopping focused population as a whole. As a cross section of our society, they have the same diversity of political views.
Finally, the journalistic value of blogs is vastly overrated. The forums they provide do provide a form of online democratic discourse (but then again, so does talk radio), but they are invariably biased and, as a result, their stories highly filtered and not vigorously vetted. I have many friends who'll skewer FOX news (which deserves it), then email me an editorial from some obscure blog. Blogs are recreation, not news sources. If the censorship described here is actually happening, I doubt that it's significantly hampering our troops ability draw their own conclusions.
I agree that this administration has put our military in a terrible situation. Rather than spending time kvetching about why some corporal can't log into Wonkette, why not log into the websites of various military units, which provide some remarkably frank, first hand reports of what is actually happening over there? After all, there are 130,000 voters over there...and over 200 million voters here. Which group needs to be better informed?