To reproduce:
1. Open attached project "FullKinematicContactBug.zip"
2. Play "test" scene. And watch how moving "Player" object interacts with other 3 objects.
3. Stop the scene.
4. In Hierarchy, select "Player" object, and in Rigidbody2d component, uncheck "Use Full Kinematic Contacts".
5. Play scene again. It plays the same way as if "Use Full Kinematic Contacts" was checked.

Actual result: only the first (Dynamic) object is pushed. No contact (collision) with Kinematic or Static object.
Expected result: when "Use Full Kinematic Contacts" is enabled, kinematic/kinematic and kinematic/static collisions should be allowed.

Repro with: 5.5.0f3, 5.6.0b1

"Use Full Kinematic Contacts" was added in 5.5