"Due to the government shutdown, FOIA/PA requests or inquiries submitted to the FOIA/PA Office will not be addressed until the office reopens." That's America's National Security Agency breaking the bad news that thanks to the lack of appropriations there'll be even less disclosure than usual about what the intelligence community is up to in your name.
The actual spying itself, however, will continue. That's essential.
The entire essential/nonessential breakdown is a fascinating semiotic window into national priorities. The official criteria for determining what services are exempt refer to ideas like the protection of human life and property. But the operational definition of these things is that if you have a gun and a badge and a uniform, you're almost certainly "essential," while if you merely feed pregnant women and newborn children, you aren't. Whether it's genuinely true that the DEA's activities are more life-protecting than WIC's activities doesn't really enter into the calculation. It's more that the violence-oriented branches of government have higher social status in the United States than the helping-oriented ones.
By the same token, of course, we've addressed and largely rescinded the aspects of sequestration that were hampering air travel. The aspects of sequestration that are hampering child care services for poor kids and their parents remain in place. These crises draw out the real priorities of the country.