Can I use a zero-waste reverse osmosis filter with a water softener?
I own an RO system and it is fed solely with soft water.  The mineral content in soft water is less fouling to the RO membrane than my hard utility water, and the membrane lasts several times longer than it otherwise would.   I predict you will have no compatibility issues with your zero waste RO system circulating a small amount of water through your hot water loop.

That said, I am not a fan of the zero waste RO systems.  RO systems require regular maintenance and if the filters are not sanitized and changed regularly, the system can become fouled with bacterial slime.  With a zero waste system, that bacterial slime is recirculated into the whole house water supply instead of being flushed down the drain.

I prefer an electric booster pump or a permeate pump to reduce RO waste water:



These provide a more positive shut-off when the RO pressure tank is full, and although they are not zero waste, they do significantly save water over a basic system.