See quotation 1840. The term is still used in the sense of uncompromising.
1840. The base of the line was the company of Straight-Outs. They are the representatives of a hardy race of honest log cabin pioneers, who, however ridiculed for their primitive manners, never fail to make their influence felt at the ballot-box.Nashville Whig, Aug. 17.
1860. You could not get this floating body of opinion on a straight-out nominee of your party.Mr. Keitt of S. Carolina, House of Repr., Feb. 1: Cong. Globe, p. 651.