Cars fragment neighbourhoods and reduce human interactions in physical ways (more1) and "Mobility Culture" has more general effects on the sociability of the culture, noise and pollution and constant traffic discourage outdoor, front-verandah, balcony or yard lingering, from which much interaction with passing locals used to occur; but there are yet other effects on the social fabric.
The trauma costs to the social fabric of collisions are incalculable, there is the grief cycle, there is also the sense of injustice by relatives who have a loved one killed and see the perpetrator, to their minds' clearly guilty at least of manslaughter, being given a token prison term and at most a few years of driver's licence suspension, by judges who are members of the middle class car culture and perhaps drive irresponsibly themselves, and aren't inclined to judge themselves harshly. Employers and other holders of power are imputed with a punitive duty of care, paying out damages of thousands of dollars to litigants who slip on a floor or receive a papercut reading a magazine; but the power of the car is exempt from any concomitant responsibility for the brain damage, paraplegics and quadriplegics it causes on a daily basis. The car culture can, and does under the all embracing alibi of "accident", get away with murder. This defines an iniquitously dominant group and throughout history such disproportion has eroded the legitimacy of institutions in the eyes of victims, relatives and perpetrators, and therefore the stability of society.
Cars, in their role of exacerbating consumerism, also contribute to the inequality of wealth and their proliferation accompanies a growth in wealth disparity. This is because they are a major expense, the second largest domestic investment, and consequently transport consumes a large proportion of people's income. This means that income they might otherwise be saving, and building up capital or assets with which they could compete within capitalist production, are drained in consumption, leaving those already with wealth in capital positions. Any independent venture must run a race to earn more than the interest it pays on borrowed money, thus paying the rich who, without being more efficient or taking major risks, remain wealthier than the entrepreneur. Most ventures lose this race, even though as self funded ventures many more would be viable.
The expense of cars gives rise to insecurity, drivers are exposed to risk because they are putting their investment in the car onto public roads exposed to collision, vandalism, theft, and to legal suit by richer more expensive car owners with whom they may collide. This insecurity contributes to selfish and mercenary behaviour and to violence and road rage (ya toucha my car I breaka ya face), plus the refined more middle class financial violence that is perpetrated through lawyers and civil damages suits. All this behaviour undermines social relationships and the general social fabric. This exposure is obviated and social relationships improved by a public transport culture.
Whilst there are exceptions, in general the car hegemony demotes non-drivers to the status of second class citizens by physically structuring the city to be inaccessible, and often downright dangerous and hostile, to them. This means that the impetus to own and drive a car becomes a priority in peoples' lives whether they can afford it or not, and this financial pressure leads to a basically mercenary approach to social interaction. Attitudes and behaviours previously only common among the greedy or criminal have entered normative behaviour. (more2) This tendency toward an abnormally high acceptance of exploitative attitudes not only degrades the social value of the person (s/he can't not be "on the make" in relationships even if s/he would want to, the behaviour is too ingrained, creating the notorious "rat-race"), it also translates into all the affairs of the individuals and even up to the international relations of the nations that possess a car culture.