...like our world, except every human begins life as female and changes to male around the age of 35 to 40, remaining so until death. (Leading to the mutations of those being born male or changing early/late.)
Already it is hard to imagine humanity standing much chance of surviving its primitive period. Such an odd and limiting window to breeding might hamper early humanity's growth potential. However, under such adversity, and given humanity's strong adaptability, it would certainly change everything about society as we could imagine it being brought to modern times, were it able to prosper.
How we consider gender roles and how they'd continue to change. Views on sex and reproduction. Religion... Would there even be anything like marriage? Fatherhood and motherhood would be seen entirely differently.
Breeding and marriage might be two different paths of relationship. With a narrow window for procreation bearing fruit, it would probably be some form of mandatory or mandated function for society. Maybe like a retirement track, where the last decades of a person's life is either donating to a sperm bank or a pick of various candidates, with various coupling rituals (or whatever they want to call it).
P.S. The reverse isn't a world I think I'd like to imagine.