As natural as water flowing downhill, for two reasons, both stemming from the fact that genomics will increase life expectancy and quality. There will be one heck of a lot of extra time. Without something as interesting as science to enhance and expand the enjoyment of a life expectancy increased by eighty extra years, life would become very tedious and boring. Secondly, all will have plenty of reason to appreciate science. Science will have provided something tangible which arbitrary and abstract belief systems had not, namely long life.
Longer life means more time.
More time means more opportunity to contemplate and to understand the patterns of life. People will have seen that marginalization of science had been a disingenuous attempt to prolong an outmoded socio-political system. They will be less willing to give up a longer life in defense of socio-political systems which had primarily benefitted elites. In the search for any avenue which may prove to be lucrative, they investigate science. They ask what science can give them.