The problem is that you are using $\theta$ in both cases, but on the left side, $\theta<0$ (according to the first image), so the sign works out either way. You have changed the sign of theta without changing what the sign of the torque means, which is why the sign error pops up.

Obviously, the torque does change signs as the pendulum crosses the equilibrium point; this is what lets the motion change direction. The important conceptual point is that the torque always acts to move the system towards equilibrium.

An analogous problem would arise for a horizontal spring-mass system, where you you look at the mass on the right and set up $F=-kx$, but then you switch to defining $x$ to be measured from the left while still defining positive force as being to the right. Then you would arrive at $F=kx$.

The problem is that you are using $\theta$ in both cases, but on the left side, $\theta<0$ (according to the first image), so the sign works out either way. You have changed the sign of theta without changing what the sign of the torque means, which is why the sign error pops up. In other words, in your second attempt you are trying to use a left-handed coordinate system for $\theta$ while still keeping a right-handed coordinate system for the torque.

Obviously, the torque does change signs as the pendulum crosses the equilibrium point; this is what lets the motion change direction. The important conceptual point is that the torque always acts to move the system towards equilibrium.

An analogous problem would arise for a horizontal spring-mass system, where you you look at the mass on the right and set up $F=-kx$, but then you switch to defining $x$ to be measured from the left while still defining positive force as being to the right. Then you would arrive at $F=kx$.