"Do you believe in" X is a badly-formed question: belief comes and goes with emotions, state of health, sleeping and waking and under external influence.
Any external influence which generates images, or alters our body state, can shape or shake the steadiness of believing.
The proper question concerns whether X is real.
However, in modern secular mainstream culture the question "do you believe in..." is regarded as primary - and the matter of whether X is actually real is subordinated.
This happens because modern secular mainstream culture is nihilist: which is to say it does not believe in reality except as a product of belief: which is merely to say - in a different form of words, since belief is labile - that it does not believe in reality.
Belief is therefore vitally important to secular culture: indeed belief is all important.
From this comes the fixation upon sincerity (or authenticity) as a primary virtue and the primacy of hypocrisy as the ultimate sin: the idea that it is not important what you believe but that you believe (strongly, self-consistently, permanently).
Sincerity and consistency and strength of belief is, for moderns, the only reality.
And when reality is based on nothing firmer than the subjective state of believing, then the stability of the world itself is experienced as being only as great at the stability of that state of belief.
This fact is vital for us modern Western intellectuals, who have been - from an early age - emotionally corrupted such that the common sense of the ages sincerely strikes us as absurd.
Hence we cannot have a spontaneous primary belief in that which has - for all of historical humanity, and still for most of the modern world - been taken as obvious: the soul, Natural Law, the supernatural, and so on.
About such matters, we cannot (even when we want to) achieve that steady subjective state of believing which forms the (only) foundation of modern culture.
(Perhaps we could, surely we could, believe-in these basic human presuppositions if they were supported by culture; but when the mass of ideas and images from the mass media/ education/ officialdom propaganda apparatus subverts these basic human presuppositions, then such beliefs are experienced as too insecure to serve as foundational.)
Of course, the state of believing is very important indeed; but belief is not meant to serve as the foundations for life.
When conceived as a here-and-now emotional conviction - belief is properly a second-order phenomenon.
Life should be built on reality, not belief.
"Do you believe that X is real?" gets much closer to what should be being asked.
From this it follows that we ought not regard as true that which we believe; but should instead strive to believe that which we believe is real.