Ha, no, definitely not! I had another immigrant friend here (before my social circle went up in flames :P ) who was annoyed by that too, & all the USians here we know are similarly bemused/grossed out by it. & clearly it's not poisonous, b/c the whole UK eats off dishes w/the residue of dish soap, & maybe the practice started as a way to save water but... I dunno. If so there have to be other ways to conserve. I mean, even dipping them in a basin of clean water? Not just the gross "one quick shake to get some of the suds off, & if there are still bubbles on it, no worries, stick it on the dish rack anyway" thing.

I almost made liseuse (who is English) choke on her coffee once by telling her I'd wondered if UK dishwashers had a rinse cycle or not.