The boring answer is that we'd use different materials for construction. Or we'd find a way to make them suitable for construction, like how we turn sand and gravel into concrete, or pack snow into ice blocks.

Concrete may be hard, but it can't deal with tension that well, this is why we add rebar to it, it makes it able to deal with enough tension that it gets useful as a building material.

The same principle would apply to pillows, pillows are soft and squishy, put them in a vacuum bag and suck out the air, and you wiuld have a pillow and a plastic bag turned into a sort of a brick.

In construction we modify the raw materials to fit the purpose we need them to.

This is a very unique question. I've never seen it in the other place or anywhere else.

Probably people would just pack materials harder into brick molds and carry on as usual though.

I imagine we'd start harvesting bone a lot.

sandbag igloos? theres earthships made with car tires and sand bags etc. helps to be partially underground.

We build stuff with clay all the time. The adobe empire will rise again (no, not that one)

Tall skyscrapers wouldn't be a thing. I think we'd see more buildings with Pentagon-like proportions.

Wood is one of those materials. If it's soft and squishy as lumber, it follows that the trees it is cut from would be likewise. So, no super tall trees.

Reinforcement with the less plentiful harder materials like we do with rebar in concrete I imagine.

Food would be interesting if teeth were soft and spongy.