For one, the people putting up those statues generally don't identify with the ones being pillaged, but the ones doing the pillaging. He's not idolized worldwide, but primarily in Mongolia, where he's viewed rightly or wrongly (there were periods of unity in the geographic area before him, and periods of division after him - but ethnicity and national identity are fluid categories, and the modern inhabitants of Mongolia consider themselves Mongolians, not Xiongnu or Rouran) as the founder and unifier of the nation, and his reign was remembered by the people who benefited from it as a time of victory, prosperity, internal peace, and world-spanning empire. And when you're a national hero, atrocities get overlooked.

I'm not sure if there are statues outside Mongolia, but much of the Eurasian Steppe remained in the Mongol Empire for a long time and were still ruled by rulers of the Genghisid lineage long after the empire's unity had ended. These areas supplied large contingents to the Mongolian army and many people living there grew wealthier as a result of Mongolian rule, and also had rulers with an obvious interest in legitimizing their dynasty's origins, so Genghis was often remembered fondly despite the brutality of his initial conquests - don't know if they put statues up, though.