Longitudinal twin studies have demonstrated that 30-50% of differences between people in terms of cognitive ability and personality traits are attributable to genetic causes -- a fascinating set of findings, to be sure.
What about trust in others? It sure seems like some people are naturally trusting and willing to be vulnerable while others are naturally skeptical and self-protective. What causes such differences between people?
Unlike cognitive ability and many personality traits, trust in others does not have a significant genetic explanation. It appears the propensity to trust is better explained by stable belief structures established through our developmental experiences (i.e., Were you loved and nurtured by your parents?) and by relationship-specific characteristics (i.e., Does this person behave in a manner worthy of trust?).
If a team member doesn't trust you, don't blame their genes. Instead, focus on the dynamics of your relationship and what you need to do to earn their trust.