There is too much data saying the best way to raise children is with a married two parent opposite sex family for it to "go out of fashion". For the upper and middle class in the West, divorce rates are down and marriage rates stable ... we just need to get it to the lower class that needs its stabilizing influence most.
What I do see due to more women waiting too late to start families and relying on genetic donations, single women using artificial insemination to have a child when they can't wait any longer to find a partner, etc is the growth of a population whose official genealogy doesn't match the genetic one. And we're already seeing people using genetic genealogy to try to fill in that missing data.
The role of surrogate mothers is already a point of contention, with some nations outlawing it while others like Canada say "only on an altruistic basis". I expect demand for surrogates to continue while other nations ban it for fear of exploiting poor women because of how many young women have STDs and will only find out when they try to start families it has left them sterile unless they get a surrogate. You'll likely see more cases of grandmothers giving birth to grandchildren and female relatives bearing children because of both demand and laws worldwide that make that almost the only legal surrogacy option in some nations.
Unless and until we can genetically engineer embryos from scratch, the demand for donor eggs and sperm will remain strong. And that raises the risk of accidental incest. We've already seen super-sibling sets from popular sperm donors. You could see genetic testing required to prove you aren't an accidental sibling before two children of lesbians via date. Or "tell me your donor number before we kiss".