If you took the photos from the same place into the same direction the perspective is unchanged - so a perspective correction should calculate the same correction Parameters for all. I would expect slight differences, but an exact match eis even better
So if everything is ok you should be able to align them In gimp.
Even slight differences in the parameters can cause different dimension of the rotated and sheared image and autocrop will likely give different results.
Better yet: if you’re sure the images should have the same corrections because they were taken without moving the camera, do the automatic fit on one and just copy the module parameters to the rest.
I think it is possible for it to get distracted if the contents of the image are slightly different, or an effect of one of the modules is slightly different. The last point is key: the algorithm could be too sensitive to certain elements; e.g. CA correction (not confirmed, just an example).
Last time I encountered a problem, the culprit was AMaZE. When I switched to another demosaicing method, the auto correction was more reliable. Lastly, I recall there being a revision in the works. I haven’t checked the status of that endeavour.
The lens correction should be the same for all photos, if no parameter changes, you should get the same result.
But, the perspective correction tries to find structures in the image to do it’s correction. So, from one image to the other, the detected structure can change and the applied transformation changes.
To solve your problem, you should apply the same set of transformation to all images.
The workflow should be:
Take a reference picture in your set
On that picture, apply the lens and perspective transformation
In the light room, select that picture, and via the history stack module copy the lens and perspective correction modules
In the lightroom, select all pictures of your set and paste the lens and perspective modules.
Retouch all images as you which.
This process will ensure that all images are processed with the same transformations and all of them should end with the same size.