When people who don't like the British call them "Brits", and people who don't like them Americans call them "Yanks" and so forth, these nicknames are loaded and hostile. As with all the others listed.

The slur doesn't lie in the names themselves, but in the way people feel.   And, of course, even if terms like "British" or "American" are used instead, that doesn't really change anything. If the feelings are hostile, those are just as loaded and hostile.
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"Sweaty" as rhyming slang? I suppose that'd be "sweaty feet" or "sweaty socks". But what's the rhyme?