Every time that happens, they cut the most essential first to protect the least essential. Hence spending money to block off WW2 monument and whatnot.
Yup.
It's actually a sticky wicket though from either side. An example I have some expertise on is scientific satellites. Trump slashed the satellite budget in his proposed FY18 budget, predominately to cut "climate change" spending. He was right and wrong. Data from many scientific satellites was absolutely used for political agendas. However, that doesn't invalidate the importance of the raw data for actual science.
While some knuckleheads may have been using data from a sat that measures ocean temps for some "biased science", that doesn't mean the raw data were unimportant or invalid for many other analyses. It's just that somebody had clout to retask the sats for stuff the previous administration was big on. Further, if you kill off an ocean temp sat (for example), you're not just killing off SST (Sea Surface Temperature) data. These satellites are typically multi-use. So while the main sensor may be for SST, it will also have other sensors for meteorological stuff, and even SAR transceivers, so you could actually be putting lives at risk.
In the same way an agency would protect their non-essential stuff* if given an option, from the other side of the coin, just slashing can do more damage than good. In the satellite example, Trump would have done better getting more expert opinions and doing surgical strikes on how the sat data were/are used rather than nuking entire programs. It's also kind of an inefficient waste to say, "we're done with this satellite" even thought it may have many more years of life as something other than disused space trash.
*The old saw about the Air Force comes to mind. The standing joke I always heard from AF people I worked with was that when you build a new base, you always put the bowling alley in first and the runway last. That way when you run over budget, well, you can't not have a runway on an Air Force base, right?