I have a feeling that the reason it might be closed in the render and open in the viewport is because there isn’t actually a keyframe that is being recorded on the mirror side.
I can see in the images that you don’t have autokeying enabled. This means that it has only updated in the viewport but that change has not been saved.
When you hit Render, it reads the animation data – ie not the same as the viewport if that isn’t keyed.
Perhaps that’s what’s going on?
And I hope that makes sense haha