I’d argue that the notion of respecting ‘a person’ (while certainly a convenient conversational shorthand) is ultimately misleading if you treat it as more than a convenient shorthand.
Saying that you respect someone is far less unwieldy than saying “I respect qualities X, Y, and Z that the person has; and they don’t have any sufficently negative ones that I need to express qualified respect of the ‘I have to respect his dedication; but not his goals’ flavor”; but it’s arguably what you mean. If people were just respected because they are respectable, you end up meaning basically nothing by it.
That said, there do seem to be several different flavors of things you can respect:
You can respect properties that are seen as desireable; but not ‘good’ in a moral sense(eg. you can respect somebody’s knowledge of mathematics or a program’s stability). You can also respect good-in-a-moral-sense attributes, but only when moral agents possess them. Finally, the oddball category is respecting ends in the sense of viewing them as desirable and being moved to advance them(like “human rights”).
In the first two cases, people become respectable by the fairly obvious means of possessing qualities that are respected. If their overall collection of qualities is good enough, you can just say that you ‘respect them’ without further qualification; if they are a mixed bag you usually make sure to qualify your statement “Fred Phelps is a terrible person; but I have to respect his willingness to stick to his principles even when it alienates potential allies.”
In the last case, that flavor of respect arguably never inheres to people at all; but it may compel you to act toward them in certain ways, or at least express a wish for them to be treated in certain ways. If I respect rule of law, refraining from dishing out vigilante justice is something I do in deference to my belief that rule of law is a desirable goal; not because of any flavor of respect I have for specific people.
As for what people who demand respect or flip out because they are being ‘disrespected’; I’ve never been all that sold on the coherence of the idea. Some of them simply seem to be dressing up a demand for obedience or a certain amount of grovelling in nicer sounding language. “Respect” sounds so much nicer and more reasonable than “endure your position beneath me on the dominance hierarchy”; and making your demands sound like something that any decent and reasonable person would agree to is a classic negotiating tactic. Believing your own lies just makes you extra sincere about it.
The somewhat more sympathetic(sometimes accurate, sometimes not; but at least not pure sophistry) demanders of ‘respect’ are the ones who are advancing an argument either about the actual distribution of qualities we both agree are respectable(eg. we both respect diligence and hard work; but the janitor believes that I have no clue how much diligence and hard work go into cleaning the office between when I leave in the evening and when I return in the morning, so I do not give him adequate credit for the virtue he does possess) or about what qualities and ends ought to be respected(as in the perennial spat between people who respect your right to hold your beliefs and people who demand that their beliefs be respected because they take them really seriously).