When animating, is there a way to stabilize the line thickness when using [Stroke Size Reduction]?

Please use the [Size Map].

[Stroke Size Reduction] uses screen space as the basis for computing lines. Because of this, depending on the curve settings, lines can look unstable when animating.

[Size Map] uses the object's UV coordinates to specify line thickness, so stable lines can be drawn when animating.
Please have a look at the [Size Map] file "LineSizeMap.blend" included in the sample files.