Based on my knowledge, there are a few things that could cause the first and last frames of your PNG sequence export to not match when you have physics (dynamics) on the whiskers:
Physics simulation starting fresh
Physics simulations naturally start from a rest state and need time to "settle in" to their animated motion. This means the first frame might show the whiskers in their initial rest position, while the animation continues from there. To address this, try using the Warm Up setting in the export dialog. This plays the animation multiple times before exporting, allowing the physics to start in motion rather than from rest.
Include Last Frame setting
Make sure you have the Include last frame checkbox enabled in your PNG export settings. When unchecked, the last frame is omitted, which is useful for some looping animations but might not be what you want in this case.
Deterministic physics
If you're working with physics constraints on the whiskers, you might want to check if there's a Deterministic option available in your export settings. This helps ensure consistent physics simulation results.
The fact that you mention the whiskers specifically have dynamics suggests physics is the likely culprit here. The Warm Up feature should help your physics simulation reach a stable state before the export begins, which should make your first and last frames match better for a seamless loop.
Try adjusting the Warm Up value to a higher number (like 2-3 repetitions) and see if that resolves the mismatch between your first and last frames.