How can I clean or renew my dining room chair cushions?

Have you tried a steam cleaner that has upholstery tool?

I don’t know what rubbing is and I would just reupholster them myself. Get some new upholstery fabric and go over the old if it’s not too nasty. Just need a staple gun to borrow if you don’t have one. If not then my best stain remover has been Spot Shot for stains. Aerosol can with orange lid. Not their general carpet cleaner but the one for stains. Yes I’ve used it on fabric as well as carpet.

get fabric remnants and sew bib style quilted chair pads that tie on, you can also buy chair pads like,''patio chair pads, at any Pier one or Home goods ... get creative ...make little tie on skirts to drape over the seats...or if your rich enough, send them out for professional cleaning , rug cleaners may even do it in your home , as a service with rug cleaning.

I completely agree with Kelly. Spot Shot is a lifesaver. It has taken out stains in my vehicle seats from the kids that a professional couldn't remove.

Without seeing a picture of the cushions, it is hard to say for certain, but as you mentioned the 'rubbing' it sounds to me like the fabric is worn down beyond rejuvenation, and is fraying. I would say that the cushion coverings need to be completely replaced with new.