Baking,
To check that Sentinel Hub works well and that the images are well aligned I searched for a mount and I did a test with Active GIF Creator and another with GIMP that you will find attached.
Results:
1. Confirmation that Sentinel Hub works well, that there is no alignment to be made and just change the requested date. Clearly by being careful not to move the image afterwards and taking images with a lag of a multiple of 10 days
2. The image of Active GIF Creator is more compressed, which can induce the effects you have reported (so I would switch to GIMP)
Conclusion:
1. When we change the date in Sentinel Hub he will provide a new image using the coordinates of the old one, so it is he who will align the images and the result is good
2. The alignment treatment of Sentinel Hub it may not be perfect (there is nothing perfect), but it is probably safer than a manual treatment on our part, treatment that should be reserved, in my opinion, only for cases for which we do not have (this is the case with Polar View images) or if it is bad.
In any case I can point out in a technical note accompanying the next images, if it seems useful to you: the method used, the URLs used and the possible treatments of the images