My goal is to take a world population grid (2.5 arcmin) and perform zonal statistics as table inside country borders (and also inside the cells of a 1-degree fishnet intersected with country borders). I see on the tool description that one shouldn't use geographic coordinate systems for Zonal Statistics as Table. However, I just tried to project my input raster to an equal-area projection and it seemed like it would never finish - also projecting required me to choose a "resample" option - I want the same values that I started with!
So, will I be okay if I perform ZS as table in my starting system (which I think is WGS 84)? I just want to add up pixels inside shapes. I'm most concerned about allocation happening properly across borders - of the countries and fishnet. And I don't understand why projection matters in this case, as my raster grid cells have a specific location and my polygons do too, so no matter what projection, wouldn't their relative placing remain the same?
Bonus question: does projection matter for plain Zonal statistics, too? What about for converting a polygon to a raster?