After installing this mod, whenever I try to load Factorio, I get an error message saying exactly: "Failed to load mods: Reached ID limit for trivial-smoke. The game cannot contain more than 255 instances of this prototype due to hardcoded limits of the engine".

Yeah, disable this mod, or go in your mod setting file (In mod directory) and set the new enemies option for Rampant to false.

Can't use this + the Rampant new enemies

So, by disabling Rampant new enemies, does that mean I'm stuck with only vanilla critters, or does it mean I get older versions of Rampant enemies?

Once you've turned off the new enemy variations (which I think are different than the regular/old), you can disable this blockable mod, and you should be able to turn the new enemies back on.

Alternately, it's likely easier just to set this mod to false in the mod list file to begin with.

I'm not struggling with disabling the mod, that's easy. I was just hoping there was a way I could make it compatible with everything else, without sacrificing content. Thanks, though.