Non-slip mousepads still slip on textured wood.

Yes, they can. The rubber base is designed for smooth surfaces. Textured wood creates tiny gaps that break the seal, so the pad shifts when you flick your mouse.

To stabilize it, a thin desk pad underneath works best. The desk pad grips the wood, and the mousepad grips the pad. Alternatively, a damp microfiber cloth under the pad adds just enough friction without sticking permanently. Double-sided tape works but leaves residue.

You could also sand the desk smooth, but that feels like setting your house on fire to roast a marshmallow.