I'm quite sure it's already scared away customers. I'm one of them.
I have 'missed' a number of opportunities over the years because I was unwilling to implicitly endorse unethical behavior (instead of quietly continuing to do business with entities I believe to be bad actors, I cut them out, because there are more important things than convenience and money). I don't plan to change this pattern, and I know I'm not the only one.
The real question is what percentage of potential future customers Uber is losing. If people like me are a tiny minority, this may not affect their bottom line at all... which I would find very sad.
If they keep scaring away engineers and getting bad publicity, will be scare away customers too?
Or will the trail of engineers eventually catch up with the quality of the experience?