I cannot quite imagine what kind of society you are talking about. Parents of young kids (younger than 5 year old?) are taking care of them at home, and those who don’t have kids and whose kids are old enough do work?
Athlete cannot have kids until they quit, but most of them are still young enough to have kids, so not so much a problem. Many of scientists should interrupt their research at least for 5 years for 1 kid, or 6 years for 2 kids, which might be a big problem for individuals of them, but maybe not so much for entire society. Politicians, same? Farmers cannot take care of their farms. They can ask it to someone else, or farming is done by companies or cooporations and farmers are employees, so it’s ok? Companies maybe need some office workers. Or, computers do the work? Then there should be some engineers. Musicians can continue practicing at home while taking care of their kids? Parental leaves of 6 years for teachers, firefighters, police officers, soldiers, civil servants, doctors, nurses, salespersons, caregivers for elders, may be not so much problems? Industries of productive manufacturers and construction need to give 5 or more year parental leave to their workers too.
Assuming typically a couple have 2 kids with 2-year interval, they take 7 year leaves, while they are 20-40 year old. One third of people age 20-40 don’t work, then are there enough labor force for required minimum jobs? While they don’t work, minimum necessities are supplied by government?