So I installed the whole Picker suite at once, and I soon realized that, for some reason, red/green wires connections go haywire when I use blueprints. (Like, everything connects to every other pole, whether medium, substation or big.) Note that I use a lot of other mods so I'm not sure that Picker alone is at cause here, even though it's the main one.
I soon noticed the auto circuit shortcut and disabled it. Certainly, it made it so it doesn't happen with poles I placed by hand… but it still happened with blueprints.
After that, I decided to uninstall the mod that was causing it. So I tried the Picker mods one by one, and the last, most unlikely one was Picker Belt. I don't know why these circuit functions are part of this mod, but whatever. The short version is that, whether by default or because of a mods incompatibility, it makes it impossible to use blueprints since it totally messes up blueprints' circuits.
I really like the functionalities of this mod, but I can't use it because of that. So either a fix, or moving these aspects to another submod (since it has nothing to do with belts) would be great.