We give a complete description of 2-local real uniform isometries between $C(X,\tau)$ and $C(Y,\eta)$ where $X$ and $Y$ are compact Hausdorff spaces, $ X $ is also first countable and $\tau$ and $\eta$ are topological involutions on $X$ and $Y$, respectively. We show that every 2-local real uniform isometry $T$ from $C(X,\tau)$ to $ C(Y,\eta)$ is a real uniform isometry whenever $X$ is also separable.d
