<i>"The angry can not find me, yet the proud goes to my door."</i>

>! Angry people tend not to listen reasoning but when they're proud of something they have achieved they want to hear praises.

<i>"My tail eludes me, when through the wind I soar."</i>

>! Probably a reference to The Doppler Effect, eh?

<i>"My shrines are east and west, my drums alert my master."</i>

>! Shrines and the cardinal points refer to ears on the sides of one's head. Ear<b>drums</b> transmit the sound to the inner ear eventually the brain gets alerted.

<i>"But give me a dollar value, and you'll lose me even faster."</i>

>! One dollar is not much. If you do not value your hearing high enough and protect your ears during loud activities then you will definitely lose it.

<b>Thus I believe the riddle pertains to:</b>

>! hearing.