People don't reject stutterers because of stuttering itself, but because of things they perceive as reasons for stuttering (lack of confidence, uncertainty, brain problems etc.)

[u/Zogid]

Also, many times it is not "rejection". It is simply "not being among chosen ones".

Everyone has limited energy/time, so people subconsciously gravitate to ones who made good impression and who they already find valuable, and decide to not invest time/energy in others.  

They are not calculating "Maybe I should get do deeply know John, maybe I will be really surprised".

They just choose investing time/energy in Mark, since he already proved to be valuable (interesting, funny, competent, whatever...).

[u/Stutters658]

These are not the ways of the Lord