When my electric mining drills run our of sulfuric acid (because I deleted the pipe), they are showing yellow dot instead of red.

This will happen if there are minerals still under the mine. It only turns red when the minerals are exausted. (edit: or out of power)
If you don't have enough Sulfuric Acid, then I believe it should turn yellow. If you are completely out of minerals in that spot, then I believe it should be red.

Isn't it inconsistent with other cases? Sulfuric acid is an input for the drill, normally when a machine is input-starved, the icon turns red.

You are probably right. It does also turn red when out of power. Maybe the mod owner can answer that. Normally I only want to see it red when out of minerals. And I like it to be yellow when paused for any other reason. Maybe we need more colors, like orange to show that it is missing power or fluid.

Hmmm... A fourth setting specially for mining drills that need fluids is an interesting option.

In regards to "out of minerals" - checkout AutoDeconstruct mod. One of my favourites, however it doesn't deconstruct drills over uranium in order to not break the pipes connections.

I use that as well, but use NoFluidstoMineUranium mod to move the fluid usage from mining to a later stage. I do need water for mining Quartz though. (Simple Silicon mod.)