""She does get involved "politically" when she meets heads of state and other royalty.""
You are misunderstanding the remit Gnu.
When she makes these foreign connections, she is representing the UK as a whole, and she is the only apolitical representative head of state.
What she cannot and does not do, is to represent any political party within the UK. She is above and outside of internal politics, so never represents government or opposition or their interests.