The deeper point here isn’t in fact about GDP, nor women working. It’s that near all of the economic numbers we use are not, in fact, the measurement we’d really like to be making. They’re nearly always proxies — something that is close to what we’d like to measure but not actually the thing itself. This means that we shouldn’t be using our economic numbers as targets in quite the way we often do.
More women going out to work for wages would raise GDP. So what? GDP isn’t the thing we want to maximize. More people being able to do more of what those people want to do is — we want to maximize human utility. We have no measure for human utility, we use GDP instead. But GDP is that proxy and so we fall into error if we try to maximize the proxy — GDP, instead of the actual target — human utility.
Which leaves us with the actual answer here to female labour force participation. We must have a system whereby if women wish to work for wages, they may. Equally, if they prefer to run their household, then so be it. This applies to men too, of course. Maximizing the choices that can be made maximizes utility, not maximizing GDP.