Error message "Your client does not support opening this list with Windows Explorer" when you try to "Open with Explorer" on a SharePoint document library in Office 365 site

[Symptoms]

When you log on to the SharePoint online site by using your
Office 365 account, navigate to a document library and click “Open with Explorer” button on the
ribbon, you receive the following error message:

Your client does not support opening this list
with Windows Explorer

[Resolution]

To successfully make “Open
with Explorer
” work, we need ensure the following:

1. WebClient
service is started 

WebClient service which the WebDav protocol enables Windows-based programs such
as Windows Explorer to create, access and modify Internet-based files.

Important Note:   If you are running a
server type Windows OS, for example, you useWindow Server 2008, install Desktop
Experience
feature first to get  WebClient service installed.

    1. From the Start menu, point to Administrative
      Tools
      , and click Services.
    2. Scroll down, right-click WebClient, and click Properties.
    3. In the Startup type list box, click Automatic.
    4. Click Apply.
    5. In the Service status section, click Start.
    6. Click OK.

 

  2.    You have supported Web browser

For a list of supported Web browsers and support level
information, please visit:
Plan browser
support

From the page you can see it’s recommended to use 32-bit Internet Explorer 7,8,9.

Note: “Open with Explorer” may not work if you have 64-bit
Internet Explorer and 64-bit Microsoft Office installed.

 

3. Add https://*.sharepoint.com
to Local intranet site

To configure Web browser, open “Internet Options” menu,
navigate to the “Security Tab”, and add https://*.sharepoint.com to Local intranet site.

 

Then restart the browser and try it again.

=======

> If you have tried the above methods, however “Open with Explorer” still does not work,
try to make sure you have applied the latest updates on the system.

> In addition, you can also try to enable Basic authentication on
the client computer, by setting the BasicAuthLevel registry entry of
the following key:

HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\WebClient\Parameters

For detailed
steps, visit the following KB page.

You cannot connect to a document library in Windows
SharePoint Services 3.0 or Windows SharePoint Services 2.0 by using Windows
shell commands or by using Explorer View
https://support.microsoft.com/kb/841215

 

If none of the above resolves your issue,  you can open a post for discussion in Office 365 community or contact Microsoft Support. 

https://community.office365.com/en-us/f/154.aspx