A Republican majority Oregon Legislature actually selected a Democrat for U.S. Senate on January 19, 1909.
This event occurred prior to the 1913 ratification of the Seventeenth Amendment to the United States Constitution, which established direct election of Senators by popular vote. In 1909 it was still the state legislatures that selected senators, and the Oregon Republicans were under no legal obligation to send Democrat George Chamberlain, who had received a plurality of the popular vote, to the Senate.
But having finished two stints as Oregon’s Governor, George Chamberlain, had established a reputation for bipartisanship.
He managed to secure the election because voters had elicited promises from legislative candidates that they would elect the senatorial candidate who received the largest popular vote. Chamberlain’s election was a test of legislators’ willingness to follow popular will in senatorial contests and helped establish a national trend that culminated in the ratification of the seventeenth amendment in 1913.
Both parties had different profiles and affinities back then. I don’t think you can equate them to their modern counterparts any more than you could equate the current parties to Whigs and Tories.