The argument that "the gap disappears when accounting for gender-specific choices" is made as an explanation of why the gap exists, which is entirely different to an argument that the gap is not significant. Such an argument would arguably be specious; the income gap is obviously still there and arguably it has negative social effects, so offsetting it via gender-dependent redistribution could well make sense.
I've generally found people on HN to be sensitive to the nuance, but over on reddit - where the level of discourse is lower but perhaps more reflective of everyday conversation - things are very different. Some use the choice explanation to dismiss the finding as not problematic, or to push the blame onto women. Some recent examples after a quick search:
If we accept that explanation then we get a lot more nuanced situation than just "it has negative social effects". A lot things have a negative social effect, but it is very rare that a redistribution is the right policy to solve it.
A gender-dependent redistribution would depend on which data we want to use. If for example carer choice is included, then we have a gap in work related injuries and death. A hard problem to redistribute. If numbers or hours at work is included we would need to redistribute that too, including overtime, and in regard to sick days women spend 50% more of that so gender-dependent redistribution model would also have to account for that.
The biggest problem I see however with a gender-dependent redistribution model is that the distribution curve is not flat. The top 1% look very different than the bottom 1%. If we look at introduction wages alone we get close to 0% pay gap in most industries, with some that overpay men and other that overpay women. A common finding in gender studies is that the bottom 10% and top 10% is dominated by men, with the top 1% being exceptional outliners, which if the same is true for income means that a gender-dependent redistribution would either need to be very dumb or be applied based on such distribution curve.
If we include pay gap to mean all income, including those with zero income, we get problems that a homeless man is treated equal to a home spouse where their partner is a millionaire. A gender-dependent redistribution should also account for this basic context.
This is why that explanation has so profound effect on the discussion. It basically makes a gender-dependent redistribution policy impossible. A bit like how crime policy in regard to gender, race and immigrant status is profoundly changed if we accept the explanation based on social economical status.
