To sidestep an issue as to not take a side.
The term was popularized in politics by Teddy Roosevelt. Contrary to what some may believe, the term is not meant as a gendered insult. It is called pussyfooting due to the quiet and stealthy way cats walk.
If a politician were to remain noncommittal on an issue in order to avoid backlash, it could be said they were pussyfooting.