(edited from previous description)
I was upgrading to the Spine Unity 3.7 runtime today with Unity 2018.1.6 and ran into this exact same(?) issue, and the delete / reimport suggestion temporarily solves it - I can add the animation to my scene and it works fine. However, when I save and exit the project, the Attempt Reimport button re-appears when I relaunch it.
The only thing in the project that I can imagine might have some side effects that cause a behavior like this is that I'm using asset bundles, though I've made sure to rebuild the asset bundles after fixing the reimport issue.
The same issue does not happen with a brand new project and the same Spine animation, so presumably the issue is project specific, though I can't imagine how. When I launch, there are no Spine related errors in the console. Are there any other debug logs that Spine might emit that might shed light on what's going on?