Question: I would like to organize a game playing session for 140 people in the same room. I could just split them up into lots of small groups and organize a tournament. But then I started to wonder, are there any massively multiplayer non-online games? My restriction is that any material needed will have to be printed out.

Answer: 
Let's walk through this. Our starting state is:

> 
> **Gnome** is enchanted by **Colorless Pledge**.
> 
> 
> 

The following events occur:

* You cast a second Pledge, targeting Gnome
* Pledge resolves and attaches to Gnome

The state of the board is now:

> 
> **Gnome** is enchanted by **Colorless Pledge** and **White Pledge**. Gnome has Protection from White (except Colorless Pledge) and Protection from White (except White Pledge).
> 
> 
> 

Now, the active player would receive priority, and so state based actions are checked.

* All White auras except for Colorless Pledge are moved to the graveyard. White Pledge is moved to the graveyard.
* All White auras except for White Pledge are moved to the graveyard. Colorless Pledge is unaffected.

Your final board state is:

> 
> **Gnome** is enchanted by a **Colorless Pledge**
> 
> 
> 

At the end of the turn, the Colorless Pledge becomes White again, but remains attaches because an exception was specifically made for it.
See Kevin's answer: the second Pledge causes the first to also grant protection from white.

If somehow both Pledges are colorless, and then both stop being colorless at end of turn, then my original answer applies:

Both Pledges will go to the graveyard, for exactly the reason you state. As soon as the Gnome's effect ends, state-based effects are checked and both auras are enchanting an illegal permanent. The Gnomes have two "instances" of protection from white, each of which doesn't remove one copy of Pledge of Loyalty, but not the other. Since all state-based effects are checked at once, both Pledges go to the graveyard simultaneously.