WARNING: This may very well be the simplest, stupidest, easiest guide to figure out yourself yet....
But it hasn't been posted!
[SPOILER]Now, simply all you have to do is visit this website, and you will be able to use the Neutral Auction house while being at a reputation that allows the Bruisers to attack you.
If you are in fear that this website is a phisher due to the fact that it immediately asks for your WoW username and password, fear not, for it is the official World of Warcraft Armory.
Before continuing, visit the site I linked you to above, and click on neutral, rather than Alliance/Horde (depending on your faction.)
You may now use the Neutral Auction house =)
Uses for this one may ask?
The first thing that popped into my head was this, (and the only thing I'm going to share,)
If you are trying to send gold from one faction to another, post auctions with one account, and buy them with a second, or a friends on the opposite faction.
[/SPOILER]
I warned you!
Have a good one.