When splicing neutral wires in junction boxes, can I use white electrical tape?
Tape is not a thing for splices.  You should not be using tape as your primary way to splice, period.  That is illegal, unsafe and will get all your work flagged by the inspector.  Since you say you are in the USA, wire-nuts and splice blocks are readily available and dirt cheap, though you can solder if you really want to.

However, the solder method you want to use is not allowed inside conduit or conduit bodies, and if you do it inside a junction box, you still need to leave 6-8" of tail.  Part of your wire will be a stiff stick, so it'll be hard to stuff into the box.  4-11/16 boxes will help, those are much cheaper at real electrical supply.  

Also, as far as taping after the solder -- that is not an afterthought.  It is complicated!  Electrical-grade soldering is serious business, and not least is the fairly complicated taping of insulation, that involves both friction tape and electrical tape.  You'd need to find an olllld timer that worked on K&amp;T to educate you.  

Shrink wrap might be a viable approach, but watch out for sharp points that wear and puncture the shrink wrap.  Part of the friction tape's job is to remove all possibility of that. 

In any case I wouldn't depend too much on NASA guidance in that most of their vehicles are single use. I would wire the way NASA's facilities department wires their boring old office buildings. Call them up, they'd be gobsmacked that anyone cares about what they do.  

That is not to say there's never a reason to use tape.  If you solder, it's an i,portant part of splicing, and you must do hots and neutrals.  Some people also use tape to over-wrap wire nuts to "keep them on", but they need to get better nuts and use the right size!  Older (20 year old) nuts are not nearly as good as today's.  Exception: nuts capping off a single wire need to be taped or they will fall off.  

Work must be neat, workmanlike and consistent within your installation.  Nobody ever got fired for using black for everything. However that can make the wiring rather difficult to understand, which is why I own 10 colors of electrical tape. 

By "consistent within your installation" I mean that if the previous work used colors a particular way, continue doing that if you are able.  If unable, use what you have, but make it plain you are doing that. 

Do not use bad tape simply to get a color.  By "bad" I mean low quality or tape which is not UL/CSA listed for use as electrical tape.