If I hear someone suggest that (say) homosexuality is immoral, my immediate reaction is to label them 'intolerant'. But that would clearly be a mistake according to the explication above. Most anti-gay conservatives are willing to tolerate homosexuals in the weak sense of allowing them to co-exist (though the political actions of some may put strain on the 'harmony' requirement). The fact that they don't respect (approve of) homosexuality is an entirely different matter.
In a pluralistic society like our own, tolerance is more than a virtue - it's a civic duty. I don't think the same can be said of respect. It might be virtuous to respect others (within reason), but I don't think it's obligatory in any strong sense. It certainly isn't a political obligation; who we respect is none of the State's business.
I note here that I mean for the possible subjects of toleration to include not merely people, but also ideas. (It's clear that the Nazis were intolerant of Jews; but a useful definition must also extend to less extreme cases.) That is, one can be intolerant through refusing to allow an idea to openly co-exist in the 'marketplace of ideas'. "Political correctness" may be seen as intolerant in this way - it seeks not to critically engage harmful ideas, but to quash them entirely.
Such ideological genocide may sometimes be warranted (however distasteful I may find it). At least, I wouldn't want to rule out the possibility a priori. Occasionally right-wingers can be heard to complain, "But you're being intolerant of my intolerance!", as if their opponent was somehow inconsistent or hypocritical because of this. I think Doing Things With Words has the right sort of response to this:
I'd tentatively suggest a criterion like this: we tolerate all and only views that are themselves tolerant under this criterion. Aside from indulging my love of recursion, this criterion lets us exclude both intolerant views and views that tolerate everything. That seems worthwhile, since it lets us avoid charges of relativism.
For the sake of freedom, you are not free to sell yourself into slavery. This is no contradiction, it's a necessary protective measure. Similarly for tolerance: we cannot tolerate the intolerant. Were we to do otherwise, tolerance itself would suffer - and the rest of us with it!
A similar case could probably be made for a widespread respect which is still selective enough to disrespect the disrespectful. Politics aside, we might well have a moral duty to subscribe to such a rule. I'm not sure about that though, I'd be curious to hear others' thoughts.
So, what do you think? Where should we draw the line(s) between respect, tolerance, and full-blown ideological warfare?