SHOULD we respect each other's beliefs? What makes a belief worthy of respect?

[Jack]

Beliefs are necessary for us to craft a working model of the world around us, but they need to be flexible to allow adjusting for new knowledge and information.

I agree, but the question implicit in the OP is whether or not we should respect all beliefs. If by respect we mean to not question or challenge, then I'd say no, no belief is beyond examination. Perhaps the only belief common to all people that we should respect in that manner simply because we can't very well challenge it is the belief that we exist, "I am".

[Cephus]

Beliefs are necessary for us to craft a working model of the world around us, but they need to be flexible to allow adjusting for new knowledge and information.

The problem is, far too many people use the most generic definition of "belief" and if they can find anything positive about any "belief", then they apply that positive to all of them and demand equal treatment for them all, from the most useful to the most absurd. The religious use the same tactic with "faith". Everyone has to have "faith", they claim, therefore since we all have "faith", all faith must be equally good and useful.

It just ain't so.

Not all faith or all beliefs are created equal.

[sulh-i-kul]

Jack, I thought the OP used the standard definition of respect (esteem, courtesy). Implicit in the question "What makes a belief worthy of respect?" is the notion that some are and some aren't. I very much doubt it was implied that some beliefs are beyond question!

Saying that he doesn't care if the sun is a ball of burning gas

I didn't say that.
I think it would be great if it was shown the Sun might somehow be burning actually. But I'm not holding my breath...

I've deliberately said things which might seem nonsensical to some people. But they don't seem nonsensical to me. Nor am I lying as the other poster seems to assume.