HOW TO SORT PHOTOS BY DATE TAKEN IN SHARED ALBUMS?

You can only sort albums you create yourself.

• All predefined albums, created by Photos, are having a fixed sort order, depending on the special album. The menu item "Sort" will show you the fixed sort order in gray. "All Photos" for a quick access by the date you added the photo, so it is sorted by the date added. Most other predefined albums are sorted by the capture date.
• Shared albums are having a misleading name. They are not really albums. The are a stream of photos that is arranged by the order you are adding the photo to the stream. Any new photo you drop into the stream will be added at the end, so the recipients will find them easily in one place. The shared albums are meant to be communication channels for exchanging photos, not as web galleries. The way the shared albums are meant to be used is to drop a few new photos into the shared albums. The recipient will get an alert that there is a new photo. The recipient admires the photo or photos, adds a comment, and replies by adding a new photo. Now you admire the new new photo, click the like button, add a comment, add the next photo a few days later. This dialog will be shown in your Activity stream. If the shared albums could be sorted, it would mess up the conservation and move the comments out of context. Previously the shared albums have been called "Shared Photo Streams". That has been much clearer, because nobody expected them to behave like albums.

if you want to create a shared album that is sorted by the capture date,

• you have first to create a standard album.
• Then sort your photos in this album by the date.
• Then create the Shared album and add each photo separately to the shared album by dragging it to the shared album. This will be a lot of work. You must not drag several photos at once, or the sequence might get mixed up.
• if you want to add a comment to have a title for each photo, add the comment to each photo immediately after adding it to the shared album. Otherwise the sequence of photos on the corresponding web page may change.

SO HOW DO I DO THIS ON MAC & IOS? ESPECIALLY IN A SHARED ALBUM.

This is a user-to-user support forum. Apple's participation here is minimal. Also, sot the shouting by typing all in caps is shouting a bit, rude. It's also harder to read than regular sentence case.

On my Mac, if I look at the entire photo library, they are already sorted by date. If I look at one of the albums I've created, I can select it by going to View>Sort. All the albums on my iPhone are sorted by date automatically. I don't use shared albums so I can't answer for those.

Here's a graphical representation of what users can sort and what the Photos app presorts: