Either wait until the shaman has built a bridge or jump across the unstable platforms to reach the cheese, then wait for the shaman to build a bridge back. There are small invisible platforms underneath each of the tipping platforms, and some very skilled mice are able to jump across them to get the cheese. The picture below marks spots that mice are able to jump on.
In the case of rushing, when mice just run towards the cheese, most commonly the group ahead will make it, while the mice behind them will fall to their death. The lucky ones to reach the right side then will wait for the shaman to build a bridge across the gap. In the case where the shamans are dead, experienced players will try to make their way back by jumping on the invisible supports, however due to the weight of the cheese this is almost impossible most of the time.
Either place planks across the un-tipped platforms (unlikely, due to rushers), or build a bridge across the open gap after the platforms have fallen. There are invisible supports at the center of each tipping island, so some shamans try to drop unanchored planks across the invisible supports.