Firstly you are burying the lede here by focusing on the meaning of the word "conspiracy", and secondly, the definition of the word encompasses acting in harmony to a common end, even if that end is not illegal.
You also ignore my point about illegality being whatever a biased court says it is. If the legal system won't recognize illegality, such as in the case of Antifa, BLM or vote rigging, than for all intents and purposes what they have done isn't "illegal", even though it clearly is illegal.
So like, running a political campaign is a conspiracy...