Our environment now includes birth control. Most people in the current population do not feature traits to overcome birth control. There is a subset of the population which does have the needed traits. This well-adapted subpopulation will grow rapidly because birth control is a very strong selection factor. From an evolutionary perspective, the correct use of birth control is equivalent to the death of offspring.
Remember that evolution is not inherently slow. It is usually slow because the existing population is typically well-adapted. A simple thought experiment demonstrates that evolution can be fast: we would all have blue eyes if the others were executed.
Given the severe selection caused by loss of offspring, evolution will rapidly overcome birth control. Just a few generations might mostly do the job. Within 500 years, birth control will simply not be a factor in human population.