I appreciate that you qualified the generalization as "a lot of" government work. I wanted to take this moment to mention that I've often seen tech circles to sound dismissive of government work altogether, as somehow less valuable/meritorious than industry, and I think that's unfortunate.
For someone who moved back to industry (from an amazing small team, working on positive federal programs), and thinking startups were probably the way to go for impact and being able to wield many skills, two of the barriers during the search were:
* It was hard to find startups with missions that I felt good about working on. Like many people, I work very hard, bring a lot of capabilities and potential, and want more than a paycheck and a lottery ticket. Scrolling angel.co blurbs was disheartening ("like Uber for embedding marketing insight electrodes into babies' brains, now with blockchain ICO").
* I heard some dismissive comments of some accomplishments simply because it was in the context of gov't, and some other times strongly suspected those dismissive sentiments (when I'm pretty sure the same accomplishments at a random startup would've been seen as very impressive)... and then I'd see comments on HN seeming to express the same prejudice. I don't know how prevalent that prejudice is, and it's far from the worst prejudice in the world right now, but it seemed to be a barrier.
Although I did eventually get offers from three startups working on good things, the process of finding them was so miserable, that I think next time I'll instead start by looking at 2-3 of the FAANGs and some other large organizations. Maybe the larger orgs, having institutional experience with much larger numbers of employees, might be less susceptible to prejudices of interviewers than at the average startup? (Well, that might be wishful thinking, but prejudices can take generations to erode, so, in the interim, doesn't hurt to mix up the approach, as a possible workaround.)