If there are one or more actions take and the net effect is no effect, what is a word for this?
There is an expression that could provide an answer. The 'zero sum game' sounds as if it might fit the bill, but in its origin, from game theory, it relates to something slightly different. The idea was to explore games, such as chess, in which either one player wins and the other loses, in which case the sum is zero - i.e. (+1) + (-1) = 0. It is possible to extend this idea to embrace your idea that the net sum of actions taken by one individual have the same number of positive and negative outcomes.
There is an alternative expression: 'zero-sum outcome'. That might do, but I have not so far been able to track down examples.
You could in theory take a chance and use the expression. I am sure it would be understood. You can signal that you are stretching the meaning of the expression by putting it in single quotes (sometimes called 'scare quotes', to show it is being used in an unusual context.
You almost have the word ineffectual which in the Oxford Dictionary means
Not producing any significant or desired effect.