It’s not like new culture wars won’t be started and fought just the same. But there was a time when slavery was the topic of a fierce culture war in the US, and it wasn’t resolved until it broke out into a literal war. Now, nearly two hundred years later, it’s still unacceptable to suggest that people who look different are better off as property rather than people. Even Florida’s attempts to whitewash Southern slavery doesn’t go so far as to blame the slaves weren’t people.
They’ve lost this culture war, just as they lost the fight for slavery and later to keep the population segregated. They’ll try again in time, but for the moment, the question of abortion and homosexual rights is largely settled at a cultural level. The conservatives lost, and that’s why they’ve largely moved on to nitpicking the definition of gender and trying (unsuccessfully) to defend their legal victories on women’s reproductive rights.