Cat 5/6 in same conduit as power: is NM-B required, or is THHN acceptable?
You mean 800.133.  And this very concept of mixing comms and power is highly improbable.  I know you're casting around for a way to do this, but this sort of "hopeful reading" is very highly prone to confirmation bias.

NM-B is always useless in conduit

Using NM-B in the conduit wiring method is not illegal, but buys you nothing but headaches.  It's very difficult to wrestle, and takes up way too much space (counts as a round wire of the wide dimension).  It's not going to bring you closer to running comms and power in the same conduit. 

As a rule, NM cable in conduit doesn't buy you any advantages at all.  This is one warning that you may be barking up the wrong tree. 

800.133 only affirms a case that's already allowed.

Elsewhere in NEC there is a rule that you can run low voltage or comms wiring in Class 1 methods, and commingle with power lines, if and only if the entire comms circuit, every inch soup to nuts, is wired in Class 1 wiring methods. 

It's not even really an exception.  You see, Class 1 wiring has no minimum voltage. If you want to install to mains spec and then run 6V on it, be my guest.  Nothing says you can't use class 1 wiring to convey signal instead of power, and that's exactly what happens between some smart switches, for instance.  The only exception being made is use of smaller than 14AWG wire.   Here's an example: 


  We have a furnace which is built to include an air conditioner.  It
  includes a 24V transformer.  Power to the furnace uses the conduit
  wiring method as does power to the air conditioning unit; the route between these units is continuous class 1 wiring method.  We can run
  the 18AWG, 24VAC air conditioning control cable through that conduit because the entire 24V circuit is insulated for mains voltage and entirely contained in a
  Class 1 wiring method.  That's an open-and-shut case for the exception, right? Right? 
  
  Oh wait, the thermostat. That is not rated for mains voltage and the wiring to it uses a non-class-1 wiring method.  Since its wires connect conductively to some of the aforementioned wires, this is no good.  None of the circuitry can share conduit with mains wiring.  


Presumably, you want your ethernet cables to exit class 1 wiring methods at a faceplate, then proceed via the decidedly not-class-1 ethernet cable to your most definitely not class 1 Ethernet card or dongle.  So like my thermostat, your entire comms circuit is not in class 1 wiring. That is exactly what you can't do.

Also I believe Ethernet cable is not insulated well enough and not a large enough wire diameter.