It’s generally not recommended to hang your bike by the dropper post for extended periods of time, as this can put excessive stress on the internal components of the post and potentially damage it.
While clamping to the dropper post stanchion while working on your bike is not ideal and some manufacturers recommend against it because it is possible to crush the stanchion tube with clamping pressure, we’ve had no issues doing so consistently for short periods of time with any post. You will, however, want to clamp lightly and wrap the post in a rag or use rubber jaws to avoid scratching the post stanchion. Like with suspension components, scratches on the post stanchion can cause premature wear on seals and introduce dirt and dust into the dropper internals.