Are there examples of the green beard effect in humans?
Your examples are way too broad. A green-beard effect only applies to the effects of a single gene or group of linked genes, not to just any trait. Racism and your Mongol war example are too complex to be explained by this effect. In reality examples will mostly be found in single-celled organisms where expression of a single protein can have whole-organism effects such as causing aggregation, or in larger organisms where some highly visible effect is possible such as a colour change.

There are very few real known examples of the green-beard effect, but four are listed on the Wikipedia page:


The killing of red ant queens carrying a particular allele by workers with a different allele (Keller &amp; Ross, 1998)
Altruism in social amoeba resulting from homophilic adhesion of a protein (Queller et al., 2003)
A multi-locus example in which similarly-coloured male lizards protect one another (Sinervo et al., 2006)
A neat example in yeast whereby individuals sharing an allele for a particular locus selectively aggregate, preventing those without the allele from benefiting by proxy from their trait (Smukalla et al., 2008)


References


 Keller L, Ross KG. 1998. Selfish genes: a green beard in the red fire ant. Nature 394: 573–575.
 Queller DC, Ponte E, Bozzaro S, Strassmann JE. 2003. Single-Gene Greenbeard Effects in the Social Amoeba Dictyostelium Discoideum. Science 299: 105–106.
 Sinervo B, Chaine A, Clobert J, Calsbeek R, Hazard L, Lancaster L, McAdam AG, Alonzo S, Corrigan G, Hochberg ME. 2006. Self-recognition, color signals, and cycles of greenbeard mutualism and altruism. Proc Natl Acad Sci U S A 103: 7372–7377.
 Smukalla S, Caldara M, Pochet N, Beauvais A, Guadagnini S, Yan C, Vinces MD, Jansen A, Prevost MC, Latgé J-P, et al.. 2008. FLO1 Is a Variable Green Beard Gene that Drives Biofilm-like Cooperation in Budding Yeast. Cell 135: 726–737.