Sorry OP but your parents seem stubborn rather than actually struggling with anything. You say they don't 'like' using debit cards and they 'like' to take cash out. I'm afraid they're adults and as adults we all have to do things we don't like.
It is ridiculous (especially in pandemic times) that your mum is going up to a cashier at a bank to get cash out rather than using an ATM. It's time wasting, unnecessary and selfish. It might be THEIR money but for the cashier it's THEIR time being wasted and THEIR life that your parents are compromising with unnecessary contact. If you parents want that much control over THEIR money they can keep it under a mattress, but when you sign up to a bank you agree to their terms of usage and if their policy says cash must be withdrawn through an ATM, not face to face, your parents need to do this or find a new bank which has policies they like.
RE the cup of tea, again I think they're being ridiculous. A cafe is well within its right, again especially right now with a pandemic, to refuse to take cash and even to insist on contactless payment (as it's not the kind of place anyone will be spending £40+). Even outside pandemic times if a place wants to be 'card only' that's their right as much as any other place that is 'cash only'.
I get why they might have a fear of contactless but it's one that has been mitigated time and time again with thousands of cases of banks proving they give refunds if a card is stolen and the contactless feature used to spend money. I get people don't like change but we're progressing as a society and that involves change, people can't be stuck in their rut and refuse progression just because 'they don't like it'. Yours is not one bit a concern for AGEUK because it's not a matter of elderly people being disadvantaged because they're incapable of engaging with a debit card/contactless, it's just a case of your parents not wanting to, and if they make that choice they have to live with the limitations this puts on their life.
There are all kinds of free cards out there which have a contactless feature so it's not a case of it only being fancy accounts that allow it. Cards like starling and monzo you can even transfer a small amount into and just keep topping up as need be, so you could put £30 on there for teas/coffees out, bread, milk ect and just top it up as you run out. Then no more fear of losing all your money if your card gets nicked, it's no different from losing £30 in cash if your wallet got stolen, actually it's better because 99.99% of the time the bank will refund it.
I'd be fine with a cashless society but don't see it happening anytime soon (too many corrupt politicians paying for their prostitures and drug habits in cash for the government to ever actually legislate it or allow it to happen completely), however you can't insist private businesses keep taking cash because some people prefer it when it'd be far more of a benefit to them to be card only. You can choose to protest this by using a different business that does accept cash but ultimately given how well it's working now I can't see this changing any businesses mind. If your parents want to resist progress and change by insisting on using cash that's fine but they can't expect the world to accommodate them and will have to accept the limitation on them if they limit how much they'll engage with modern society.