Diablo 2 successfully had both open and closed battle.net options for decades, and while technically map hacks were still not allowed, I’ve never met someone who was banned for having them, or any other hacks, on open battle.net. It was fine, and gives people who want to hack a place to do so without needing to bother other players who tried to play legit.

You can see videos of turbohud used with d3 on youtube. It adds, for example, item/skill texts rather than just an icon, more detailed dps meter, and a larger minimap as an overlay, etc. I don't know if any of it should be considered cheating.

Also, for what it's worth, the TH4 site says it disables itself when pvp marked.