Electrochemical concentration cells -- how anion levels change
Considering you have chosen a $\ce{Zn}$ concentration cell:
The cell representation is:
$$\ce{Zn(s)/ZnSO4(M1)||ZnSO4(M2)/Zn(s)}$$

Anodic reaction puts more $\ce{Zn^2+}$ ions in the solution:
$$\ce{Zn(s) -&gt; Zn^2+(aq) + 2e-}$$
To balance these extra $\ce{Zn^2+}$ ions salt bridge pulls some anions into anodic compartment.

Cathodic reaction removes $\ce{Zn^2+}$ ions from cathodic compartment:
$$\ce{Zn^2+(aq) + 2e- -&gt; Zn(s)}$$
To make up this equivalent amounts of cations are pulled off from the salt bridge.

So activity of $\ce{SO4^2-}$ is not changed in either of the solutions. It is only those of $\ce{Zn^2+}$ ions in both the compartments, which undergoes a change leading to redox reaction.