The correct answer totally depends upon the specific lens and also upon the manner in which you desire to use it.
Even when using a lens on a tripod, some lenses require you to turn IS off, some do it automatically for you, and others actually have IS modes specifically created for tripod use. The last category includes Canon's Super Telephoto series that are tuned to reduce the effects of mirror slap when mounted on a tripod.
Once ingrained in a particular culture, such as professional photographers, some ideas are hard to modify when the current state of technology makes those ideas outdated and in need of modification if not outright obsolete.
One glaring example is Image Stabilization. When the IS lenses for interchangeable lens SLR cameras first began appearing in the second half of the 1990s, there was an issue with vibration feedback loops when the camera and lens were mounted on a tripod. Vibration from the IS unit would cause the camera to vibrate, which would induce correction from the IS unit, which would cause vibration, which would induce correction from the IS unit, which would cause vibration...
By the year 2000 pretty much every lens manufacturer had upgraded their IS technology to automatically turn off IS when the camera was detected to be mounted on a tripod. Some lenses have even appeared on the scene that have IS profiles specifically designed to be used with a tripod. Yet more pros than not will still tell you in 2021 to ALWAYS turn off IS when you are using a tripod.