Beliefs that aren't easily testable also tend to be the kind of beliefs that have a lot of political associations, and thus tend not to act like beliefs as such so much as policies. Also, even falsified beliefs tend to be summarily replaced with new untested/not-intended-to-be-tested beliefs, e.g. "communism is good" with "correctly implemented communism is good", or "whites and blacks have equal average IQ" with "whites and blacks would have equal average IQ if they'd had the same cultural privileges/disadvantages". (Apologies for the necessary political examples. Please don't use this as an opportunity to talk about communism or race.)

Many "beliefs" that aren't politically relevant—which excludes most scientific "knowledge" and much knowledge of your self, the people you know, what you want to do with your life, et cetera—are better characterized as knowledge, and not beliefs as such. The answers to questions like "do I have one hand, two hands, or three hands?" or "how do I get back to my house from my workplace?" aren't generally beliefs so much as knowledge, and in my opinion "knowledge" is not only epistemologically but cognitively-neurologically a more accurate description, though I don't really know enough about memory encoding to really back up that claim (though the difference is introspectively apparent). Either way, I still think that given our knowledge of the non-fundamental-ness of Bayes, we shouldn't try too hard to stretch Bayes-ness to fit decision problems or cognitive algorithms that Bayes wasn't meant to describe or solve, even if it's technically possible to do so.

Beliefs about things that are outside our future light cone possibly qualify, to the extent that the beliefs don't relate to things that leave historical footprints. If you'll pardon an extreme and trite case, I would have a belief that the guy who flew the relativistic rocket out of my light cone did not cease to exist as he passed out of that cone and also did not get eaten by a giant space monster ten minutes after. My anticipations are not constrained by beliefs about either of those possibilities.

What do we lose by saying that doesn't count as a belief? Some consistency when we describe how our minds manipulate anticipations (because we don't separate out ones we can measure and ones we can't, but reality does separate those, and our terminology fits reality)? Something else?