If you use the gamingest headphones with proprietary dongles, you can get decent latency. But then you're sacrificing on sound quality or ANC, and if you have multiple devices you want to use them with (eg a console and a PC), you have to either physically move the dongle between them, or suffer with Bluetooth lag and connection hassles on one of them.
Bluetooth is still bullshit in terms of latency. It will get better with LE Audio, but whether it will get good enough is anyone's guess, and it's still in its infancy and support is almost non-existent.