What I have heard is that this idea (that all beliefs should be based on empirical evidence) has been completely abandoned by philosophers. The concept was called Logical Positivism, and it was pushed by A.J. Ayer about a century ago before being rejected (even, eventually, by Ayer himself) due to a very simple question:
“Regarding this concept that we should only believe things based on empirical evidence–what is the empirical evidence for that?”
Everyone willing to think open-mindedly on that question realized that there was no empirical evidence for it at all, and that it consequently fails its own test.
But this idea is no less self-contradictory now than it was when Ayer was pushing it. Demanding empirical evidence simply assumes that Positivism is true. It neither deals with the contradiction at its core nor gives us any other reason to accept it.
And this last brings us to the arbitrariness of the position. Insistence upon empirical evidence is simply demanding a preference for the senses over thoughts. But there is no more reason to reject the reality of mental life (consciousness, free will, qualia, moral sense) than to reject the physical.
The modern materialist would scoff at the cartesian skeptic who demanded mental evidence that the physical world exists, who claimed that no evidence which assumes the physical can be considered evidence, and who explained away everything that seems so obviously physical as “really” a mental phenomenon (presumably, an illusion of some sort).
But that position is no less defensible, if far less popular, than the materialist’s own position that we should only acknowledge the physical and explain away the mental as if it were “really” physical.
A more reasonable approach would be to reject both of these positions as arbitrary and self-contradictory demands. But this would mean accepting our mental, as well as our physical, experience as a valid source of information.
To insist that we simply reject the non-empirical until it is empirically established is to replace vast swaths of our intellectual maps with nothing more profound, or less demonstrably false, than the hollow threat: “here there be dragons”.