The hairdressers I go to ONLY accepts cash. Doing this they have kept their prices very low. I have used card payments for such things as my weekly supermarket shop for many years, but would not dream of expecting a small local shop to take that for anything under at least a fiver.
As any cash I have in my purse will have been there for weeks, it is not filthy lucre at all. Any coins I get in change, go into a different part of that purse and are kept for about a week (in isolation) before being transferred to the main coin area. I do not wear gloves when shopping (will do so in winter for warmth), but wash my hands with soap and water as soon as I return home, and after I have unpacked my shopping.
I would really be unhappy at seeing cash disapper completely. We have a regular busker spot in my town, we give them coins, younger g.children love to be given a shiny one pound coin when visiting, vending machines need coins, I would be embarrassed at offering a card if purchasing say, one cake at my local bakery. And, would also know that if people did, then they would have to up the prices of those cakes to cover the extra costs to them.
Being careful about hygiene does not mean being paranoid.