Thin sheet of lead woven into your character's attire covering either the heart or the navel depending on where this particular setting says that the soul of beings happens to be contained. Those two are the most common.
So if the spell is detecting the alignment of one's soul then that should properly protect your PC without requiring funky armor.
Sure it's fluff, but it would be nifty inexpensive fluff!
Run it past the DM, of course, since it isn't a magical solution to a problem.
Ring of Mind Shielding. Prevents your alignment for being read.
"Never argue with stupid people, they just drag you to their level and beat you in experience."