Things that are separable can be pulled apart or divided from each other. You may feel that someone's political opinions don't matter, because they are completely separable from the kind of person they are.
If you're extremely close to your best friend, the two of you might not be emotionally separable. In other words, you are emotionally attached to each other, or inseparable. But unless you're handcuffed together, you are physically separable. This adjective is clearly related to the verb separate, "move apart or form a boundary between," from the Latin root separare, "pull apart."