The lyrics of "The Boxer" by Paul Simon are often appropriate when discussing beliefs, facts, and reality.

Still, a man hears what he wants to hear
And disregards the rest — Agree-to-Disagree

I prefer the Doobies,

But what a fool believes he sees
No wise man has the power to reason away
What seems to be
Is always better than nothing

Poetic flowery language. While that's certainly useful, it's not usually a good way to do philosophy.

It's all about the relationship between the three terms in the OP. People use those three terms in very different ways.

Try this...

All belief is about what happened, is happening, or is expected to happen(events). Facts are events. Belief is always about events. Events are not truth apt. Beliefs are. Correspondence between events and belief is truth. Reality is all the events(what's happening) at any point in time. Reality is not truth apt. Belief is. Belief is always about fact/reality. Correspondence between fact/reality and belief is truth.

When a creature attributes the right kind of meaning to a particular set of events during either contemplation or observation, they formed and/or reformed accurate(veridical) belief. They've a good grasp upon the way things were, are, or are expected to be. They have true belief about fact/reality.

James has a unique approach to interpreting the connection between beliefs and reality. Materialism, for example, is not so much a fact about the universe as it is a fact about the way a certain type of person lives his life. What is a fact? In the limit, it is an isolable quantum of human experience, "this redness now." As soon as you start to expand that momentary quale, to generalize it, you lose the only true measure of facticity, its givenness. So maybe your fact becomes gravity. Then whether the quale was an apple or the planet mars, what is evidenced is the facticity of gravity. But the momentary expression of gravity in both cases is not a pure or simple thing. The apple falls under the composite influences of gravity, air pressure, coriolis force, etc.. And while the path of the planet seems to be a straightforward exemplification of the law of gravity, that is only an illusion of approximation. The three-body problem has no closed solution.

Materialism relies upon rationality for its facticity. But rationalism and idealism too are also facts insofar as they are embodied by people....

Facts and beliefs don't really differ much. Both are constructions which serve to rationalise observations/experience of reality. Both are never fully 100% certain. Both often have large dogmas connected to them and groups defined by whether they pursue one dogma or another. — Benj96

Facts "have large dogmas connected to them"?
Come on now, Benj.

Facts "have large dogmas connected to them"?
Come on now, Benj. — Alkis Piskas

Scientific dogma= being testable, being repeatable through time as a measure of veracity. Objectivity has restrictions just like subjectivity does.
Scientific facts cannot apply to anything thay is single in occurrence. Things that are exceedingly rare and cannot be reproduced according to scientific dogma cannot be a fact. However not all facts are provable or measurable by scientific means. Ethics exists as a fact of life that we cannot apply scientific method to and yet dictates scientific exploration.

Come on now, Alkis.

Fact: That which actually exists or existed or happens or has happened. Something that is known to exist or to have happened.

Dogma: An official system of principles or tenets concerning faith, morals, behavior, etc., as of a church. A specific tenet or doctrine authoritatively laid down, as by a church.

As for "scientific dogma", it's a frail term, used either in a figurative way or prone to dissolve into thin air at first scrutiny, if used in a literaly sense. It is connected to scientism, which is sinIe-minded adherence to only testable and provable facts and events, and it is as stong as dogma in religion.
For me, "scientific dogma" is whatever scientists believe that it can be explained by Science, although it has be only partly or selectively proved or it has never or not yet been proved in a definite and/or indisputable way. It is the result of scientific materialism, which makes science look like a religion.