Evolution is slow. It takes generations. Depending on the selection pressure these may be quite few. Assume sexual drive were the only determining factor for reproductive fitness (which probably is a good approximation for some animals) and you introduce a 95% successful 'contraception' (e.g. a genetic modification to avoid reproduction - this has been done for mosquitoes) and guess how many generations it takes to work around it. Now humans use 95% reliable contraceptives - but their usage is regulated by complex processes so no simple analysis suffices (just think of the misinterpretaion of the baby-bust/pill-gap).
Additionally we don't have to limit us to genetic evolution. We could also consider memetic evolution - the one invoked somewhat imprecisely in point 4. Memes evolve faster. It could happen that meme-complexes joining birth-control and anti-science out-breed progress within few generations.
Sure after 500 years we'd likely have the technological means - if anyone is still interested in technology then. And for some 500 may be a more likely date than 50.
It takes many generations. Human generations are quite long.
Without a technological civilization, the oldtime pressures of hunger and violence will dominate everything else - Which in some ways favors various means of birth control. Because having 6 kids and having all of them die due to splitting available resources to many ways is not a successful strategy. Therefore, your projection only makes sense in a continuing technological civilization, in which case engineering happens.
And again. Most people have kids. Successful use of birth control allows yo...
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