In the far future I think it's likely we will rewire our genetic code so that fertility and conception is under our conscious control rather than the current random, hit and miss situation. And for sure, we all hope one day STDs and the like will be a thing of the past.
Of course some people will resist it, you'll get the religious nutjobs who say it's playing God, and the well meaning but just stuck in their ways people who say it's just wrong because it's unnatural, will devalue sex, intimacy, closeness, etc... and no doubt that might be partly true for a time... but the eventual result, if society survives it, as it surely will given the other challenges we've faced and continue to face as a species - the eventual outcome will be that everyone is just far less repressed and more comfortable with sex, sexuality, intimacy, both physical and emotional, which can surely only lead to a more open and honest culture where people no longer feel the need to hide parts of themselves from their fellow human being.
For the record I dont think that the decisive decoupling of sex and conception will be the catalyst and deciding factor here - rather, this event will be just a part of a gradual process of expunging our innate evolutionary fear of being vulnerable in the presence of others, fear of the other, this microcosmic iteration of the tribalism that once helped us to survive in a harsh and brutal natural world but now threatens to destroy us before a more enlightened future such as the one I've alluded to above can ever come to pass.