Hello @wordmax
Hmm, I don’t think this would be a theme issue at all. The “site identity” feature of the Customiser is actually WordPress’, not ours.
I have tried a few tests and the image does get “cropped” (but not actually physically cropped) on both Blocksy and the default 2021 theme, which would confirm a WordPress issue. Check this out – https://streamable.com/g4zc83.
I do not get a “skip cropping” option either, on both Blocksy and the default 2021 theme.
Unfortunately, we cannot comment on why this happens. It would be recommended to contact the WordPress developers on GitHub (or their main trac) in order to get more information about this matter.
Hope this clears things up!
Thanks.