Most proponents of low-income housing I know of would like to vastly increase density and lower the number of SFH but the vast portion of the market and voters does not want that at all since it would lower their home value.
The more common reason people vote against it is because they want their neighborhood to be frozen in time at the precise moment they moved there; that's what they originally chose after all. And they don't want to be forced to look at anything with a FAR above 0.4, and even that much is questionable.