Is there a national White republican movement. Probably not since that would be racist.
NBRA doesn't restrict membership by race. I'm white & I belong. Many Freepers of various races have joined to support the goals of NBRA and to help fund their grassroots campaign.
The Republican Party was founded by people who wanted to abolish slavery. The Party's first candidate was Abraham Lincoln.
Here's information about the Lincoln-Douglas Debates:
http://www.digitalhistory.uh.edu/database/article_display.cfm?HHID=336
Lincoln's opponent in 1860 was Democrat Senator Stephen A. Douglas.
Excerpt:
"Douglas's strategy in the debates was to picture Lincoln as a fanatical "Black Republican" whose goal was to incite civil war, emancipate the slaves, and make blacks the social and political equals of whites."