How do people serve hot drinks to visitors in these mismatched cups?! ... Are these people also serving meals on random plates?
Honestly OP, this made me hoot! You'd have forty fits if you came round to mine. (Actually I'm pretty sure you wouldn't as it's clear you're talking about your preference in your house but...)
It's made me think about the Christmas sort-of-party we have each year. Mulled wine, mince pies, other festive food, you get the idea. About 20-30 people in the house over the course of an afternoon/evening. (I say that, I noticed last year an increasing number are turning up on the dot and staying till the bitter end).
Mulled wine is served in mismatched mugs, teacups from a matching tea service, coffee cups also matching, a couple of mismatched cups and saucers and some glasses with handles which came from somewhere.
Tea and coffee if desired are served from a teapot which doesn't match the tea service, and coffee pot ditto.
Food is served on a frankly magnificent array of plates, dishes and saucers accumulated over the years, some significantly older than me.
I'm sure there are people thinking 'blimey I couldn't handle this chaos in my house' but they do all seem to enjoy it. It's a bit of a talking point who gets what. Regulars know what they like ('spiced apple juice in a green coffee cup please'), and new acquisitions are noted.
BUT! I do actually sympathise very much with the difficulty of being given stuff. What harmonises the mayhem in my mug cupboard/dresser/kitchen in general is that DH and I chose it all (well, okay, mostly me) and love it all. That's the thread which ties is all together and it is tricky sometimes when someone thinks 'ooh Freezer loves crockery' and gives something I wouldn't generally give houseroom. (Of course sometimes I love it. ).
In conclusion I think this is an 'ill thought out gift' issue not a 'matching mugs' issue.
Full disclosure: currently banned by DH from buying any more crockery (coffee pots a particular weakness) due to lack of space.