I have been searching around the internet about this question and have had mixed results. Put simply, if I give one of the two foreign Pokemon an everstone ( So it may pass down the nature ) will this disable Masuda Method increased shiny chance? As much as I desire the shiny I will be devastated if it has a hurtful nature, but I want to make sure the everstone wont make hatching for it just as tedious as random encounters.
Quite logically, the Masuda Method would still be in affect regardless of if the Everstone method clashes with it. Therefore, it should be FIIINE. :D
Hope I helped. :) Source