It's critical that a team have similar values, some with standards a little higher than the others, in order to maintain cohesion. Too much disparity in values spells doom because the focus will not be there. When a member of the group does something that goes against the grain of the group's goal, it can be forgiven the first time as a mere oversight or mistake. However, when the behavior continues, is counter-productive and detrimental to the group's overall goal, trust in that team member deteriorates, as you have said. So fear begins to grow that the one who is not following through on their commitment to the group's goal is actually an enemy.
Enemies come in all forms.
Their work is slipshod and unreliable. Someone will have to return to that work and redo it so that it will stand muster. That is a waste of resources. The one who is obsessed with extraneous issues is another enemy. To the extent the obsessor focuses on the extraneous issues instead of the work at hand, that person weakens the strength and reliability of the group.