Final answer:
Republicans countered Democrats' racist tones in the 19th-century presidential campaigns by highlighting Democratic attempts to nationalize slavery and utilizing the 'bloody shirt' campaign to remind voters of the toll of the Civil War.
Step-by-step explanation:
The Democrats campaigned with instances of racism and pro-slavery sentiments during the presidential elections of the mid-19th century, which were reflected in the songs and rhetoric of the time. The Republicans, on the other hand, countered these campaigns by accusing Democrats of attempting to nationalize slavery through popular sovereignty, using political cartoons like 'Forcing Slavery Down the Throat of a Free Soiler' to highlight these views. Furthermore, Republicans employed the 'bloody shirt' campaign, reminding voters of the Democratic Party's association with the Southern Confederates and the Civil War's human toll. This approach also included honoring war victories and the fight against slavery, as seen with slogans emphasizing 'liberty and union' used by Republicans like Rutherford B. Hayes in campaign posters.