By default Outlook will download the data from all the mailboxes that you have access to. It’s good for several reasons to download the recent items in your own mailbox, but it can be problematic on shared mailboxes. Luckily, you can turn off sync for those while keeping it for your own.
In Outlook, go to File > Account Settings > Account Settings
Then, click through Change > More Settings > Advanced
Untick ‘Download shared folders’
You will need to restart Outlook for this to take effect.
The shared mailboxes will still be accessible, but won’t be downloaded to your computer and will be read entirely online.