I found a solution my self.
Instead of using the a negative value for the width argument in position_dodge() to reverse the order, one could reorder the factor passed to the colorargument in aes() for example with fct_rev().
library(tidyverse)
df <- tribble(~dimension, ~group, ~value,
"dim 1", "A", 0.5,
"dim 1", "B", 0.75,
"dim 2", "A", 0.4,
"dim 2", "B", 0.4)
plot <- ggplot(data = df,
mapping = aes(x = dimension,
y = value,
color = fct_rev(group)))
plot +
geom_point(size = 2,
position = position_dodge(width = 0.5))

If desired, you can define a new colour for the legend.
plot +
geom_point(size = 2,
position = position_dodge(width = 0.5)) +
guides(color = guide_legend(
title = "group",
reverse = TRUE))

(disclaimer: from a visualisation point of view, this may not make sense. The reprex is only meant to show how it is done technically.)
Reading the warning for negative width values in position_dodge(), I drew attention to this in a Github issue (https://github.com/tidyverse/ggplot2/issues/3610#issuecomment-767480561)