I had a lot of problems too with battlenet. Meanwhile i start battlenet-agent through steam, installed it in steam as non-steam-game, and config it over steam. It resolves also some of the battlenet-agent-update problems. Maybe it is worth a try for you.
Is Battlenet telling you this or Diablo IV? Some months ago Diablo IV told me that my drivers are out of date and are not supported. But I was able to play Diablo IV. Last time I started Diablo IV some days ago the message didn’t appear anymore. I’m using Battlenet in Lutris.