The liberal idea of an anti-utopia is well-presented in The Handmaid's Tale. Abortions and lesbianism are horrific crimes. Less competent men exercise total control over much smarter women. Religious hypocrisy literally runs the country. Old, barren spinsters take out their repressed spirituality on young, vibrant women. If you want to see such a world you need only tune in to Hulu.
The conservative anti-utopia would be one in which abortions were available on demand--perhaps even funded by the state. Children could go to government or school representatives to obtain said abortions, or simply to seek confidential counseling without parental approval. Gay marriage would be a basic human right, and opponents would be ostracized, if not prosecuted. Young, telegenic, less-competent religious leaders would garner large crowds, much to the chagrin of the more seasoned, devout elders. If you want to see such a world you need only open your eyes.