I don't exactly know. Seems to me like 90%...but my offices are somehow never impacted (my current project is self-funded, so not subject to budget fights), so my perception is certainly biased.
Based on traffic patterns during shutdown, I'd say it's closer to 40%. There's a lot that's considered critical or national security infrastructure that doesn't get shut down, including some you might not even think of (USDA inspectors, for example - plants can't run without an inspector on-site, so the entire meat industry would come to a screeching halt if FSIS shut down.)
There's also a slight misunderstanding that it's not just civil servants being furloughed, it's non-critical government projects being suspended, meaning the contractors get furloughed as well. HHS's 2018 contingency puts have the federal employees on furlough...but that could very well represent 2/3 of their projects, involving who knows how many contractors, plus downstream effects (e.g. researchers unable to start projects because of delayed grants.)
It all gets very messy and ridiculous. But 40%, head-count-wise, is probably a good rule of thumb.