I have a rug under my table on hardwood floors and no pad. I did this in my last house too with no problems. I really don't think you need one.

IMO moving chairs on a rug is a apin already and to have to move them on a thicker rug IMO wouldnot work

Ok great thank you so very much! Saved me $$ on buying a of unnecessarily :)

I had same question. What about the wood floor underneath? Should u have one of those that you can cut to size like from Home Goods? Mesh sort of-doesn’t change thickness of rug?

Thank you so much. I have LVP underneath. It needs an area rug in general because if I didn’t have one my floors would be ruined!!! I have little felt pads on the underneath of all my chairs and when you pull them out it leaves and awful scratch and that’s without someone even sitting on it. I couldn’t imagine how my floor would look if someone slid out their chair from the table without some sort of rug!

No pad under my Persian in the dining room. It's been on wood flooring at our current house and at the old one, with no issues whatsoever.

Depends on what the backing is on the rug. Just make sure it is safe for your LVP. https://www.houzz.com/discussions/4086590/safe-rug-backing-for-vinyl-plank-flooring

“I put a rug pad under all area rugs. I use the ones made of felted wool. We have no problem moving the chairs.”

Yes this. I purchase mine from Overstock.