JetPack does a lot of things, so it's easily likely to interfere or conflict with a lot of plugins.

There is a known conflict between the Shield's User Management module and JetPack's ' Protect' option. 

You cannot use both at the same time and may face lock outs.

Also, there is a conflict between JetPack Brute Force Module and Shield's Login Guard module.

JetPack Sharing is getting blocked

If JetPack Sharing is getting blocked when it tries to connect, you can unblock it by going to Shield => Lockdown module => and turn "Anonymous Rest API" option off. 
If the problem still remains, turn "Disable XML-RPC" option off.
For more information about these Lockdown options, read the article here.