Question: When using wirenuts to make joints, is it necessary to twist the conductors together before applying the wire nuts, and is it necessary to use insulating tape over the wirenuts?

No & No

I've seen equipment manufacturers instructions that state you must twist conductors before using the supplied wire nuts. But from the instructions I've read on wire nut packages you don't have to, although when done they want 3 twists outside the nut.

Sounds like a trick question but I'll say no and no.

What I want to know is how many more times are we going to discuss this?

It depends on whether I'm installing the receptacle with the ground pin up or down.

I will answer by saying it depends on the manufacturer's instructions. As I have seen instructions that say "pretwisting not required" and "twisting of conductors required".
I am going to try and locate the one package that requires twisting.

I have never seen the requirement of taping a wirenut.

Pierre

You must twist the bare conductors otherwise the solder doesn't stick...

as commom practice, I always twist the wires before installing the wirenut, and I always uue tape... just as a safety .

MJ what is unsafe about not twisting or using tape?