When in doubt, research:
The OED wrote:
hill-billy
Forms: Also hillbilly, hilly-billy, -billie
1. A person from a remote rural or mountainous area, esp. of the south-eastern U.S. Also attrib. and transf.
No connotation or denotation of racism or political perspective in implied in any of the citations.
The OED wrote:
redneck
[Omit the two senses of the word referring to animals]
II. Slang Uses.
3. orig. N. Amer. (usu. derogatory). Originally: a poorly educated white person working as an agricultural labourer or from a rural area in the southern United States, typically considered as holding bigoted or reactionary attitudes. Now also more generally: any unsophisticated or poorly educated person, esp. one holding bigoted or reactionary attitudes.
[citations omitted]
4. Eng. regional (chiefly north.) and U.S. regional (chiefly north Midland and west.). derogatory. A Roman Catholic; (also) an Irish person.
[citations omitted]
5. S. Afr. (usu. derogatory). = rooinek n.
[citations omitted]
Here the sense of the word is much more cleared aligned with particular attitudes.
Incidentally, the citations do not support JasonGone's suggestion about the origin. The Battle of Blair Mountain took place in 1921. The earliest citation of the term in the OED is dated 1830 from
Southern Tour by A.Royall, which predates the Battle of Blair Mountain by some 91 years. There are three further citations that predate the battle (from 1891, 1904 and 1913).
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--James