They must be first shown to be valid beliefs. Anything which contradicts non-controversial observations of reality cannot be a valid belief. For instance "If I jump, I won't fall back to the ground" would not need to be respected, because it's invalid.
It depends on the belief. But if you tolerate every belief, you'll also be tolerating intolerant beliefs (racism, homophobia, etc...). In that way, no one will elect you if you tolerate every thing, because that means you'll always promote intolerance.
Maybe ideally it makes sense that one have respect and tolerance of others (humanity?). But not that that respect and tolerance extend to their beliefs. If one believes in stoning gays I should neither respect or tolerate their belief.