Switch between working offline and working online. Click Send / Receive Work Offline. When Outlook switches between working online and offline, all email accounts are changed. You know you’re working offline when Work Offline is highlighted on the ribbon or Working Offline appears on the status bar at the bottom of the Outlook window. Click Work Offline. It's the third option in the drop-down menu. When Outlook is in offline mode, you'll see a checkmark next to 'Work Offline' in the main Outlook drop-down menu. To disable the offline mode, make sure there is no longer a checkmark next to 'Work Offline' in the main Outlook drop-down menu.
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Symptoms
In Microsoft Outlook 2016 for Mac, you are repeatedly prompted for authentication while you're connected to your Office 365 account.
Cause
This issue occurs because of the presence of duplicate tokens in the keychain.

Resolution
To resolve this issue in Outlook 2016 for Mac, install the February 2017 Outlook update (version 15.31.0) from the following Office website:
Workaround
To work around this issue, delete any cached passwords for your account, and also delete any modern authentication tokens from the keychain. To do this, follow these steps.

How To Uncheck Greyed Work Offline Outlook 2016 For Macbook Pro
Note
These steps affect all Office applications that use modern authentication.
How To Uncheck Greyed Work Offline Outlook 2016 For Mac Os
Quit Outlook and all other Office applications.
Start Keychain Access by using one of the following methods:
- Select the Finder application, click Utilities on the Go menu, and then double-click Keychain Access.
- In Spotlight Search, type Keychain Access, and then double-click Keychain Access in the search results.
In the search field in Keychain Access, enter Exchange.
In the search results, select each item to view the Account that's listed at the top, and then press Delete. Repeat this step to delete all items for your Exchange account.
In the search field, enter adal.
Select all items whose type is MicrosoftOffice15_2_Data:ADAL:<GUID>, and then press Delete.
In the search field, enter office.
Select the items that are named Microsoft Office Identities Cache 2 and Microsoft Office Identities Settings 2, and then press Delete.
Quit Keychain Access.
Note
When you start Outlook, you are prompted to authenticate.
How To Uncheck Greyed Work Offline Outlook 2016 For Mac 64-bit
Honestly, if the Out of Office options are greyed out, it sounds like the account was not added as an Exchange type account (IMAP instead).
Cached
What is the server, in-house ? If so, what version and SP level of Exchange ? Needs to be Exchange Server 2010 Service Pack 2 or later, per https://support.office.com/en-us/article/General-requirements-for-Outlook-2016-for-Mac-A07A593D-B383...
I have an account with MS-hosted Exchange (not Office 365 but the completely equivalent Exchange-only MS hosting) and this 'just works,'
both adding a shared calendar and Out of Office settings.
Switch From Working Offline To Online - Outlook
For the desired calendar, ask your Exchange admin to verify permissions settings/access for this user.