This idea of denying people who have been convicted of crimes the right to vote has been debated for a couple of centuries now. It is viewed by many as retribution for an act against society. Should it be forever?
Voters at that time did not vote directly for candidates for the U.S. Senate. The race was over who would be elected to the state legislature, which had the power to name the senators from the state. Lincoln lost the election to Douglas not because there was a sudden flood of illegal Irish voters into the electorate but more likely because the incumbent senator began with such a decided advantage in that electoral system.
The tradition of state control was one that suffragists had to overcome to get the Nineteenth Amendment (giving women the right to vote) ratified in 1920, and it was not easily done.