modernbeat

No, most shelf paper is low-tack and doesn't leave any residue. Even less chance of transferring adhesive if the table and seats are a little dusty. If you're worried, shelf paper is inexpensive at big-box stores and some grocery stores. You can try it out on your own patio table or chair before you inflict it on a table in the wild.

For occasional picnic tables in parks I use shelf paper. It sticks to even the most filthy table and doesn't go anywhere. It's a one-use item, which will discourage some. When done, it's not so tacky that it's difficult to remove. So it peels off easily.