I'm pretty active in anarchist (of the left-leaning variety) spaces and this is literally the first I've heard of family-abolitionism. That doesn't necessarily mean it ain't common, to be clear, but it does mean that this assertion that it is "common in anarchist communities" should probably be taken with a neighborhood-clearing and hydrostatically-equilibrious grain of salt.

At most, I've encountered calls to abolish the dependence on traditional family structures, in particular the assumption of a "nuclear family" baked into a lot of societal interactions. That doesn't mean abolishing families (nuclear or otherwise) themselves, but rather making it so that people who lack familial support systems (nuclear or otherwise) are not disadvantaged as a result of that lack.