I think you are NOT reflecting the poll correctly (i.e. again: debate tactics).
The poll talks about people's support to have more housing being built near public transportation, allowing the construction of duplexes, fourplexes and sixplexes being built "in all large cities" and giving homeowners the right to build e.g. "in-law suites" and "cottages" in their own backyards.
Nowhere does it say: "Are you okay that the state simply builds 'social housing' next to you."
There is a giant difference between a "sixplex" like:
And "social housing":
