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When exporting to a 1-bit raster format such as BMP, TIFF, GIF, or PNG, the background of the resultant output is black when it is expected to be white.
The background of the map is set to something other than white. There is a known problem with the 1-bit threshold when exporting with a background color that is not white.
Set the background of the map or data frame to white before exporting.