> If so, even if you don't include gender as a feature itself, your outputs may end up being biased (in the technical sense) by gender.

Part of the problem is people using the same word to mean multiple things. For instance, "bias" has a precise mathematical definition in the context of statistics: https://en.wikipedia.org/wiki/Bias_(statistics) . And this sentence makes no sense with that definition. In fact, with linear models it is mathematically impossible to make a "worse" model (in terms of mean squared error) by including more variables (like gender, age, race, etc...).

> you can't be "blind" to race, color, religion, and gender

Also I am not sure that this train of thought actually leads to where we want to go. A perfect model isn't necessarily blind to these features, a perfect model treats everyone as an individual.