FBOs - shared or no in OpenGL 3.3?

My inclination would be to make them shared, but this seems to indicate they are not? What’s the story?:

If they aren’t shared, is there any cost of calling wglMakeCurrent()? I already use a background hidden window context to share all contexts with, so I could just create FBOs on this persistent context and switch to it whenever I render to an FBO.

I am having good results switching to the persistent hidden context whenever an FBO is used. Hopefully there will be something I can do like that on Mac and Linux.

FBO cannot be shared.
FBO does not consume resources, replicate the FBO in all your contexts and use it.

Yeah, but then you have to have a map to look up the FBO by context and you have to set it up and check it each time it is used in a new context, and then clean it up when a context is deleted. It’s unnecessarily messy.

Yes, it is harder. But there is no other way. You can also use thread local storage if you have 1 context per one thread.