Is mate choice in non-human primates MHC-dependent?
tl;dr It's messy for non-human primates too. Winternitz et al. (2017) ("Patterns of MHC‐dependent mate selection in humans and nonhuman primates: a meta‐analysis", Molecular Ecology 26(2)) review studies of MHC-based mate choice in human and non-human primates. Some of the take-home messages, mostly from the abstract:


  [abstract] the overall effect sizes of primate MHC-based mating preferences
  are relatively weak ... calling for careful sampling design in future studies. 


There is a


  "systematic trend" for primates preferring MHC diversity (p. 679)


(I think this means "not significant" ...)


  (p. 680) Nonhuman primates tend to consistently prefer MHC-dissimilar mates (Fig. 4a), but our power to detect a significant average effect is limited by our small sample size (N=6) and by the addition of random effects to control for pseudoreplication.


For MHC-diversity preferences:


  Examined separately ...  nonhuman primates had a non-significant trend for mate choice for diversity (primates = 0.110 (-0.207 to 0.456), N=7, Fig. 1b)


Here are some of the key figures (these figures also include data for humans, omitted here). However, note that the overall estimates in this figure do not account for the effects of study ID and phylogenetic relatedness (see Figure 1 in the paper), which tend to make the confidence intervals wider/weaken the statistical significance.


Figure 4a, preference for MHC-dissimilar mates [disassortativity] (overall CI is [-0.01, 0.18], consistent with the "almost significant" comment referenced above)





Figure 4b, preference for MHC-similar mates [assortativity]:




For reference, the species included here are: Rhinopithecus roxellana (golden/Sichuan snub-nosed monkey); Cheirogaleus medius (fat-tailed dwarf lemur); Papio ursinus (Chacma/Cape baboon); Microcebus murinus (gray mouse lemur); Mandrillus sphinx (mandrill); Macaca mulatta (Rhesus macaque).