Such grants are funded on a reimbursement basis (or at least mine is): each month, I submit an invoice (via the scientific software 501(c)3 of which I am a part). Then NASA pays it. When the EO was announced, my guidance was simply that NASA was not going to pay out for a while and my February paycheck was just going to not show up for a while. To my knowledge, this was basically the guidance for every NASA, NSF, NIH, etc. grant. (I believe DARPA grants are not frozen.) These do not just fund what the more conservative among us might call 'mathematical wankery', they fund all kinds of things across science.
The issue is not whether some of these grants should have been issued in the first place. The issue is that suddenly, a large group of researchers is either not going to get paid, or their organizations are going to have to float their salary themselves on behalf of the federal government, because the federal government has just said that they plan to renege on their agreements. How many will miss rent or mortgage payments?
Although the order has been blocked for now, it is still unclear what it will mean for me and others. (I would submit an invoice on Feb. 1... would it be paid?) It's not like I just got laid off and can go look for other work now: the funding is likely to come back, I just get the joy of having no idea when.
For those of you who seem to have little problem with the EO itself: please take at least a few moments to consider whether your principles outweigh the real human costs here, and whether there might have been a less brutalistic way of achieving the same principles.