The likeliest culprit for the offensive reaction is the foaming agent found in almost all toothpastes. Sodium lauryl sulfate (SLS) is a surfactant -- a sudser -- added to toothpaste. It creates the froth that toothpaste becomes after you begin brushing by lowering the surface tension of the saliva in your mouth and allowing bubbles to form. While it aids in spreading the toothpaste throughout your mouth, it also creates the impression of cleanliness; a mouthful of foam just feels cleaner.
But SLS has other properties, too. For one, it suppresses your sweet receptors, so it has a dampening effect on the generally sweet taste of orange juice. In addition, SLS destroys phospholipids. These fatty compounds act as inhibitors on your bitter receptors. So by inhibiting sweet receptors and destroying phospholipids, SLS dulls the sweetness and promotes the bitter taste in orange juice.
(or until the first coffee anyway!)