57% Hispanic and 35% non-Hispanic white in 2010, voted just under 70% for Romney, but has been trending Democratic in recent years.
I'm guessing many of the Hispanic population in this county aren't citizens. 
You'd guess right. Liberal, Kansas is the center of the worst form of employment in the country--the meatpacking industry. It's basically all done by undocumented immigrants because no one would ever take such a dangerous and unpleasant job at such low wages otherwise. Some other nearby counties (Finney County in particular) are similar.
Wikipedia has racial demographics as 65% white, 24% other, 4% black, 3% Asian, 1% Native American, 3% "two or more races". Of those, 42% identified as Hispanic or Latino. That's a high amount of minorities but it's still clearly a white-majority county, and considering usually low Hispanic turnout rates it's voting patterns make some sense (it's also possible these are Texas-style, more assimilated Hispanics).
Interestingly, the demographics of the largest town, Liberal, are quite strange -- it's both more white (69%) and more Hispanic (a full 59%).
You're comparing 2000 data (for the county) to 2010 data (for the city). In 2000, the city was less Hispanic, while identification with "Other" dropped from 2000 to 2010 (probably not an actual demographic shift, just fewer Hispanics identifying as "Other" on the Census).
