Opinions are statements of preferences not based on facts or knowledge. Beliefs are acceptances of statements as fact.

These are not "my" definitions, this is how each word is commonly defined. They are, actually, lifted from the OED.

By "entitlement" I mean "justified in." If you prefer I use that term, fine, but I use entitlement because of the phrase "not entitled to one's facts."

And, as beliefs are acceptances of fact, just as one is not justified in having their own set of facts, they are not justified in holding any belief they want.

To illustrate, let's take the difference between a political opinion:

"I like low taxes because I like having more money."

versus political belief:

"I want low taxes because they will lead to higher GDP growth."

The first is a simple statement of preference, of desire. There's no acceptance of fact. The speaker might as well have said they prefer chocolate ice cream.

The second is an acceptance of a fact, that lower taxes will lead to higher GDP growth. That can be evaluated. It may not have been, but it can be. It can be evaluated either with hard, empirical data, or it can be evaluated using economic theory.

In either case, if the speaker cannot justify the belief with a logically sound and valid argument ("a good reason") then there's no entitlement to hold that belief.

This does not mean that a belief has to be demonstrably shown in order to be valid, nor does it mean that two beliefs that are logically opposed can't both have good reasons for thinking them.

It does mean that you're not justified in holding any old belief of your choosing.

I mean, you can physically hold an unjustified belief, just as you can physically live your life with your own set of facts, I suppose.

I don't see how it wouldn't be relevant, to be honest. Black salve and ivermectin are easy examples of why unjustified belief is something that should be discouraged.