Date of Shared Album photo changes to the date it is added to the Album.

Where are you checking the date? And which system version do you have installed?

When I add a photo to a shared album (in Photos 6 on macOS 11 Big Sur) and look at the info of the photo in the Shared Album, it is the date the photo has been taken. Photos 6 is saving the correct exif date for the capture date. But the file itself in the shared album is a new file, because photos is creating a smaller version for sharing, and has a recent file creation date.

The older versions of Photos did indeed change all metadata for privacy reasons, but since the upgrade to Photos 6 on macOS 11 and iOS 14 the Shared albums are a bit better at preserving metadata and even allow us to sort the photos by the date.

That's part of the security and privacy policy that Apple has. It is removing all metadata from photos posted to the Shared Albums to protect our privacy. That way no one can use the online photos to find out where they were taken.

If you need to have the info included with the file you can use comments to the Shared Album to give what info you'd like.

I think what the OP is saying is it reverts any changed dates to the dates the photos were imported. At least that's what's happening for me as well. Running the latest Big Sur. Wish there was an option to prevent it as I've backdated a lot of old scanned photos.