It's only one bit of data, but it's easily apparent if we get to ignore things like gender fluid or intersex. Sex can be inferred by appearance, name, clothing purchase, shopping history--so it's almost free data.

Although Google still thinks I'm the opposite gender, I guess I'm not heteronormative enough.

I think it's just about anonymity in research data. These are the most common variables across databasets.

More and more data is being released, specially government funded data in the US. Anonimity of respondents is a big deal. Would you like everyone to know your debt? Or your salary?

If people knew that they will be identified and their answers will be public, they may lie or refuse to participate.

As a researcher you want truthful data about a representative sample of everyone. If you exclude people sensitive to privacy, that is not represetative.

There is a trade off between respondent anonymity, usefulness of data and complexity. Take for instance the "Survey of Consumer Finances" released by the Federal Reserve. It provides quite many variables, which is useful but uses multiply imputed observations to provide anonimity. However, it's a pain in the ass to deal with multiply imputed data :(

Presumably without gender, the number of unresolvable clashes would be a bit less than doubled (allowing for even rarer multiple clashes).

Well if you work with even smaller data sets every additional attribute narrows the field quite a bit unless it is ubiquitous. Adding a species field to employee records or "doesn't have Marfan's syndrome" wouldn't narrow much but cummulative divisions of N help a lot with scaling.