Rationalism and idealism contradict each other

Socrates, Plato, Berkeley, Hume, Kant and Schopenhauer are all idealist-rationalist philosophers. In one form or another, all six deny the independent existence of matter. All six deny that matter is primary and mind is secondary. All six maintain that what we call material objects and the material world exist only in being perceived. In this sense, all are idealists, not materialists. This might seem to constitute a contradiction. If matter and material objects exist only in being perceived, then how can there be any objective knowledge of the world? And if there can be no objective knowledge of an independently existing material world, then isn't all human knowledge merely subjective? If a philosopher condemns all human knowledge to being purely subjective, then how can such a philosopher be classified as rational or a rationalist? Clearly, there is nothing rational about denying that there are independently existing material objects. If a philosopher maintains that objective knowledge or universal truths are impossible, then a philosopher who holds that position cannot be classified as a Rationalist. Yet the Rationalist-Idealist philosophers all claim that they can circumvent the seeming absurdities and contradictions. If material objects are nothing more than ideas in a mind, nothing more than subjective perceptions that have no existence apart from perception, then how is objectivity possible? Either our ideas and perceptions depend on matter and must conform to matter if they are to be objective, or matter depends on our ideas and perceptions and are perfectly subjective. So which is primary: ideas of objects or material objects; mind or matter?