Most of the monuments and markers did not have an explicit reference to white supremacy, although it was often implicit in the ritual surrounding their erection and commemoration. Occasionally there were monuments such as those of Charlotte, NC, which held that Confederate soldiers, "accepting the arbitrament of war... preserved the Anglo-Saxon civilization of the South and became master builders in a re-united country". Often the political discussion surrounding monuments was infused with white supremacist rhetoric; when the Confederate memorial was erected in Raleigh, NC in 1895 it was during a concerted push to thwart the power of the "fusionist" (Republican/Populist) movement by disenfranchising blacks. The Raleigh News and Observer cheered on the cause of "pure white Democracy", while advocating for the cause of "No Negro Rule in Raleigh."

There were also a large number of monuments dedicated to the "faithful slave" - such as this one, this one, this one, and this one - with the implicit message that the proper place of African Americans in the South was in a subordinate role.

But the most explicit dedications to white supremacy were typically made in relation to the violence of Reconstruction - don't forget that an estimated 50,000 blacks were killed by the Ku Klux Klan and other paramilitary organizations between 1865 and 1877 in an effort to prevent them from exercising their rights as citizens. One New Orleans monument to the White Leaguers - who played a similar role to the KKK in Louisiana - was dedicated to "to those who lost their lives in the act of disenfranchisement from alien and negro rule". Meanwhile, this historical marker in Colfax, Louisiana celebrates the 1873 massacre of "150 negroes" (who were defending a courthouse and elected sheriff against armed white attackers) because it marked "the end of carpetbag misrule in the South". And this memorial in Liberty Place in New Orleans, photographed by Dorothea Lange in 1936, held that "United States troops took over the state government and reinstated the usurpers but the national election November 1876 recognized white supremacy in the South and gave us our state."

So there were some memorials that did indeed have explicitly white supremacist messages, but for the most part the message was an implicit one.

For more on the history of the memorials, I'd recommend David Blight's Race and Reunion on the origins of the Lost Cause, as well as Cynthia Mills and Pamela Simpson, eds., Monuments to the Lost Cause: Women, Art and the Landscapes of Southern Memory; and W. Stuart Towns, Enduring Legacy: Rhetoric and Ritual of the Lost Cause.

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Follow-up: What about the assertion that some of these statues were put in place during the heyday of the civil rights movement as a means of asserting the position of those in the south? I could see that being true but could also see that being made up.

Where did you hear/see this?