Reading it again, I don't think the point being made had anything to do with class. The point being made wasn't 'people who rent are of a lower social class and therefore don't mind dog poo everywhere'. Neither was it 'people who don't have kids don't mind poo everywhere'.
The point actually made (rightly or wrongly) was:
- People without kids might not be as aware as those who are parents about the dangers of dog poo.
- People who rent property may not feel as attached to an area (as they're only there short term) as those who own a house in the area and therefore not care as much about fouling on the streets
It's possible/probable that both these assertions are wrong, but I'm sure the OP wasn't trying to insinuate that the lower the social class you are, the less likely you are to care about dog poo.
On another point, if dog poo gets trodden into your house from the street, I don't see why it's any less dangerous than 'poo in a park'. But maybe you need it in greater concentrations than you get on your shoes to be dangerous. I don't know.