= Solution
Keep source, observer and <magnetic field> in their original places, but interchange the physical <polarizers>, including their pass-axis orientations. The forward order is then $P_2$, glass, $P_1$, so the new <Jones matrix> is again $P_1R(\theta)P_2$. Consequently
$$
\boxed{I_{\rm swapped}=\frac{I_0}{2}\cos^2\left(\frac\pi4+\Upsilon LB_\parallel\right).}
$$
This is the same intensity change as exchanging source and observer. At the field that maximizes the original forward transmission, the swapped arrangement blocks the beam. If both operations were performed together, the original order relative to propagation would be restored and so would the original transmission. The answer concerns exchanging the two differently oriented pass axes; simply relabelling two identical <polarizers> while leaving their axes fixed would not change the apparatus.
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