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The correlated trait fallacy is having a trait that you want to screen for, and instead defining your test on a trait correlated with that one when you have a direct way of measuring the trait you're interested in.
An example everyone should recognize is minimum word requirements on essays in school. What you care about is that the essay is good; the word count is at best a symptom of quality that you can use if you don't have time to read the actual writing. So all you're doing by making the word count an actual criterion for judgement is discrediting essays that make equally powerful points in fewer words than you expected - ironically, the opposite of what you should be doing!
Politics and the English Language
Another example is distributing aid meant for the unfortunate to people based on "oppressed traits". For example, shelters for homeless LGBT youth.
Wanting to help the unfortunate is good, but why is it only for LGBT youth? That means you would turn away a homeless person for not being LGBT. Even if they're an ally. Even if they're definitely less fortunate than someone you'd accept. Oppressed traits should be a heuristic for who deserves priority, not the definition.