Summary: The stochastic Allen-Cahn equation with multiplicative noise involves the nonlinear drift operator \(\mathscr{A}(x) = \Delta x-(|x|^2-1)x\). We use the fact that \(\mathscr{A}(x)= - \mathcal{J}^\prime(x)\) satisfies a weak monotonicity property to deduce uniform bounds in strong norms for solutions of the temporal, as well as of the spatio-temporal discretization of the problem. This weak monotonicity property then allows for the estimate \[ \mathop{\sup} \limits_{1 \leq j \leq J} \mathbb{E} [\|X_{t_j} - Y^j \|_{\mathbb{L}^2}^2] \leq C_\delta(k^{1-\delta}+h^2) \] for all small \(\delta > 0\), where \(X\) is the strong variational solution of the stochastic Allen-Cahn equation, while \(\{Y^j : 0 \leq j \leq J\}\) solves a structure preserving finite element based space-time discretization of the problem on a temporal mesh \(\{t_j : 1 \leq j \leq J\}\) of size \(k > 0\) which covers \([0,T]\).