Only 50% of the time, but that’s 50% better of a guess than you’d make without knowing gender.
ZIP codes contain maybe 40K residents [0] (many contain fewer) and there have been around 25K days in the last 70 years. Sure births are not evenly distributed, but still...
I think you're making the assumption that all three data points are needed for all 87%. But obviously some people can be uniquely identified based on just {zip, date or birth}, such that gender isn't necessary.
So the distribution could e.g. be 8% same, 8% opposite, 5% both, 79% neither, and explain the original numbers without triggering the paradox.
ZIP codes contain maybe 40K residents [0] (many contain fewer) and there have been around 25K days in the last 70 years. Sure births are not evenly distributed, but still...
[0] https://www.unitedstateszipcodes.org/images/comparison-of-po...