I think the view behind the anti-car movement is that there shouldn’t be cars. Period.

I don't think so. Fuck-car people are rather against the omnipresence of private cars and how cities prioritize them instead of greener means of transportation, which creates mortal danger, pollution, wasted energy, wasted materials and wasted space. But I don't think they would mind the occasional car for reasonable usage like disabled people, craftsmen, public services etc.