Gengis Khan was lefty wasn't he?
Gengis Khan was certainly hawkish but the Soviets were generally pretty hawkish.
In terms of America conservative and liberal it is hard to measure because America didn't even exist at the time.

You put Gengis Khan in a modern context- it would depend upon if Gengis Khan was hostile to American interest. If he was anti-american or declared enemy of America, the Lefties would want his autograph and he would have face on thier T-shirts. As far as how conservative vs Liberal is generally seen in the world, it's fairly obvious that Gengis Khan fit in the left column- unless he was an anti-communist. And considering the area of the world he was in, he would probably be battling and the Chinese [and in the soviet era, the Soviets] so that is hard to guess. But in modern context, probably Joe Scarborough would be on Khan's side and Joe's dad would probably be against Gengis Khan.
But a Gengis Khan educated in the West would probably resemble a Bin Ladin- but 100 times smarter. Gengis Khan would actually win wars, unlike Bin Ladin. The Northern Alliance probably closer to Gengis Khan. Of course Gengis Khan wasn't a Muslim nor a Christian, his religion was War. He would be have more interested in West Point than some liberal arts education and working with these perverted unhonorable, flakely so called Muslims.