I wouldn't say it's slippery, but it's not rubbery/no traction. It's a canvas material, such as what you see on durable backpacks/duffle bags, some outdoor camping chairs (not cheap ones that have the tink tent material though) ect. Usually, when I go grocery shopping I fill up the back (or have them in collapsable boxes) so I can't comment on that, but I wouldn't expect things to stay in place when making a sharp turn less than if it was just carpet.
I would say if traction is a concern, buy something in addition to (such as nets that clip your stuff down) and don't make that a factor in not getting these because I can't imagine not having these now; I can throw my bikes and anything down in the back and not have to worry about it ripping up the carpet.