The Smuggler's Union is the Brethren of the Coast Trade Union faction. In order to use the Auction House in a port ran by the Brethren, a player must be indifferent or better Reputation with the Smuggler's Union. Additionally, you can find their faction leader in the Black Market in Tortuga, there you can buy titles, cosmetics, and combat items which unlock depending on if you have a trusted or better Reputation with the Smuggler's Union.
Your faction standing will be lowered when sinking merchant ships belonging to the Smuggler's Union on the Open Sea.
I decided to try the killing Varyag's to gain rep. Doesn't work at all. Completely misleading. However, I did kill a Brittish smuggler and get 10 points rep. Lvl Restrictions appear to apply. I'm lvl 50. Lvl 30 or lower doesn't appear to get any rep; lvl 40 and above does.