So, this was verified on Method (up to level 20), and is reasonable to assume would work on any server (including hostile, although it'd be far more obvious there)
If you create a new char (I know, ouch!
and never do any missions on that char (including the very first tyndall mission "introduction to the matrix" or whatever its called...
Your reputation will always remain 0/0/0 - this means that if you activate PvP by typing /pvp, no one can attack you! Conversely, you cant attack anyone else either, but you can certainly go for a Physician/Upgrade Master loadout and keep your favorite organization/faction/friends buffed up and healed
Here's a step by step:
1.) Create a new Character
2.) Use /suicide to skip the tutorial as soon as you get dropped into the first room at level 1, pop out of a hardline somewhere, and start killing mobs to level up...
3.) Never do a mission! Ever!
You can join a faction to get an organization tag on your name (which will then also allow you access to the archives), however doing this will make you appear hostile in pvp again - however you can leave the faction at any time to regain pvp invincibility!
I've not tried doing a mission with someone else leading, as im not sure how that will affect your reputation and dont want to risk it at level 20... however, neighborhood missions have no affect on reputation at all; and there are plenty to do! They are more fun than contact missions anyway...