Relatively few serious philosophers disagree with the positive component of Hume's claim: that reason is (for many people, at least) the slave the passions. On the other hand, many philosophers disagree with the normative component: that reason ought to be the slave of the passions, or that it must be so. Hume himself has a thing or two to say about juxtaposing is-ought claims in such a manner ;)
Of course, you're absolutely right about non-philosophers using "reason" and "logic" as a rhetorical cudgels. We should recognize their (poetically) broken and faithless reasoning and point it out as such.