R plot background map from Geotiff with ggplot2

Here is an alternative using function gplot from rasterVis package.

library(rasterVis)
library(ggplot2)
setwd("C:/download") # same folder as the ZIP-File
map <- raster("smr25musterdaten/SMR_25/SMR_25KGRS_508dpi_LZW/SMR25_LV03_KGRS_Mosaic.tif")

gplot(map, maxpixels = 5e5) + 
  geom_tile(aes(fill = value)) +
  facet_wrap(~ variable) +
  scale_fill_gradient(low = 'white', high = 'black') +
  coord_equal()

If you want to use the color table:

coltab <- colortable(map)
coltab <- coltab[(unique(map))+1]

gplot(map, maxpixels=5e5) + 
  geom_tile(aes(fill = value)) +
  facet_wrap(~ variable) +
  scale_fill_gradientn(colours=coltab, guide=FALSE) +
  coord_equal()

With colors: