I think the mission of the US Digital Service is fundamentally non-partisan: we want to make government work better for the American people. When a veteran can apply for health benefits online, they have a better experience. But it also saves the money from them driving to see someone in person. There's so much work like that to do that everyone agrees will make the government better, more responsive, and more efficient.
I also think the USDS has built up some reputation and trust because of the good work that it's been able to do so far. I'm heartened when folks like Kevin McCarthy (majority leader in the House of Representatives) tweet things like this: https://twitter.com/gopleader/status/796823547343736837
At Google, I didn't always agree with what the CEO decided to do, like shutting down Google Reader. Sigh. But there was a ton of important work to do, and concentrating on the common ground made it possible to do really good things.