On the crisp versions, it becomes visible that many of your assets have a lower resolution that the tile size, and not even an exact multiple of it : Some pixel columns are doubled, some are not and the effect can be jarring.
If you can't get tiles that map 1:1 with screen pixels, well, you'd rather keep the overall filtering : it will help a lot blend images of different qualities together.
The "scattered dots" and "marsh symbols" seem to be overlays of a monochrome texture. It may not be too hard to increase their native resolution, and the result will look quite sharper, even with an overall filtering on top.
Strangely, the "stone deposits" seem to be natively higher-resolution than most of the rest, as it doesn't show the same kind of issue.