to not know what to do with my coffee cup?

[HedgehogintheFog]

I love using my reusable coffee cup, especially since covid, as so many places around me seem to have defaulted to providing disposables only, even if you're sitting there to drink. However, when I am out and about for a weekend of shopping or a day out on holiday, I don't know what to do with it once I've finished my coffee. Sometimes I want a second coffee in the afternoon, but my cup is in the bottom of my bag with grimy milk and chocolate powder from my morning cappuccino. Is it weird to ask the coffee shop to rinse it out? Is it too gross to do it in the loo? If I'm in a pub and getting them to refill my water bottle, is it odd to also ask them to rinse my cup? Genuinely curious as to others' opinions.

P.S. I also have a weird thing about drinking out of paper cups (and eating with wooden cutlery), so it's not solely for altruistic environmental reasons!!

And yet, up and down the country, millions of them do, lol.

It really only takes seconds. Again only IME, but they always seem to have a device like a mini-fountain sort of thing (someone who works in a cafe can probably help me out here!) that they turn the cup upside-down on briefly. You hear it squirting water and then they place the cup on the coffee machine and away they go.

I put it in a big reusable freezer bag to carry it round when dirty. You can have two cups

You are completely missing the point about food/drink preparation areas being kept separate - nobody should be placing dirty cups anywhere near the coffee machine.
How would that work at a self serve machine where you just get given a mug and keep going back for refill coffees?

Starbucks barista asked me to put my clean, reusable cup into one of their cups so she didn’t have to touch it. I was a bit put out but actually it made perfect sense.