First I have to mention that, unless you are exporting images or video, clipping should be used sparingly. Clip as few vertices as possible for performance. Definitely don't use a clipping attachments for your entire skeleton.
If you are exporting images or video, you can specify cropping for the export rather than use clipping to define the export size. If exporting data for a runtime, you could let images be drawn outside the viewable area, without clipping. They would be drawn off screen or can be masked or clipped efficiently at runtime. In either case, it can help when animating to have a rectangle that denotes the viewable area in the Spine editor, but is not exported.
Can you explain the use case more? Isn't the background by definition fully behind the character?
A checkbox to exclude a slot from all clipping attachments may be somewhat simplistic. It handles the use case up until you need to exclude a slot from one but not others.
Would using 2 identical clipping attachments achieve the same goal with more flexibility? Eg, if you have rectangular clipping (again which should be avoided if possible) for the background, you could have a duplicate for the foreground. Your character would be between the two clipping attachments in the draw order.