Any chair type can scratch wooden floors if dragged around or moved without care, including acrylic dining chairs. However, there are ways you can avoid furniture from scratching your wooden flooring, including adding felt floor protectors under your acrylic dining chair legs.
However, you have to ensure that the felt stays on, and if it becomes worn down, re-apply the protectors. These pads come in all shapes and sizes and can be bought to fit even the most unusually shaped and awkward furniture.
You can also consider placing a rug under the dining table to prevent your acrylic dining chairs and the table from touching the wooden floor, ensuring it remains pristine and unscratched.