The Gauge Dropper in Mekanism can be used to interact with fluid or gas gauges in that mod to empty/deposit fluids/gases by left/right clicking them.

With EMI installed, it overrides the mouse click behaviour to instead show recipes or usages for the fluid/gas.

Even if the default left and right click keybindings for showing recipes or usages are changed/removed, it still blocks the dropper usage (and instead nothing at all happens when clicking).

Disabling EMI, either by disabling the mod completely or using the in-game option to disable it, makes the Gauge Dropper work normally.

Image of the gauges I'm talking about, with the Gauge Dropper hovering over it (left clicking here should empty that gauge and deposit it into the dropper, but with EMI installed it opens the recipe view instead):

Minecraft version: 1.20.4
NeoForge version: 20.4.214
EMI version: 1.1.4+1.20.4+neoforge
Mekanism version: 10.5.11

This is related to Mekanism's EMI integration and should be reported to them.

Turns out it was actually already fixed in the latest version of Mekanism, I just missed it when skimming their changelog 🤦