This article shows a scenario where the Dynamics 365 app button will be inactive, like grayed out, in the Outlook menu. This may be caused just because of the View Reading Pane configuration in your Outlook client.
However, you may still see the button active when you create a new email or an appointment:
In Outlook, your View Reading Pane must be Right or Bottom for the button being active:
Hope this helps.
This post is based on the following configuration:
- Dynamics 365 Online Version: 220.127.116.111
- Outlook 2013
Please notice there may be other reasons why this button could be inactive, see the following forum discussion.