It gets worse
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and this is also without doing the British Gallon - American Gallon thing.
UK wise I should also note that while milk will give some fractional litre value on the front then the sizes are still the classic 1 pint, 2 pints, 4 pints or 6 pints sizing (if pressed they will probably say it is old machinery or fridges were built with this size in mind), and saying barkeep I would like 6 counts of 568ml of your finest ale (UK pint is also different to US pint which is 473ml for liquids) will probably not get you terribly far. You can also usually go to a market stall or butchers and ask for something in pounds or ounces (I will have to look but they might have even been an exception to the law which mandated conversion).
Anyway I know what all the common units and their breakdowns are, as well as many conversions, but only because of the whole engineering thing and old cook books, and even then it is mainly because I do a lot of legacy parts engineering. Even with that I have no mental concept at all of how long, heavy, hot, fast... something is in imperial units beyond order of magnitude (I know a foot is commonly used for either human sized things, or in thousands for mountains or distance shooting sort of thing, but if someone tells me 16 feet I have no clue without first converting to just under 5 metres, or for really crude then dividing by 3 and maybe adding a little bit). If someone tells me their new baby weighed 11 lbs I have no clue how much that is and if it is big or small for a baby without converting, and even then I probably still don't know if it is big or small but that is probably more of a side effect of not caring about babies.
Such a thing also means I find it quite odd when some American politico gets trotted out and does the "it is measurements that relate to people's everyday lives" routine.
Possible exception in imperial units in that I can do normal car speeds in imperial if I am going from standstill -- if I am doing the just off a motorway and 50mph feels like standing still routine then probably not going to happen but I could still do metres per second well enough in those scenarios.
Speaking of cooking then nobody in the UK that has not interacted with Americans when it comes to cooking will know what you are talking about if you do your measuring in cups (a volume measurement) as everything that is larger than a tablespoon and more solid than honey (even then I would not be surprised to see honey done by weight) is done by weight or count.