Re the people asking for lifts, it's an easy one. If you don't mind, say "Yes, no worries, hop in!" If you do mind you say "Ah sorry, I can't today". You don't need to explain any further.
The number of people who can't or won't drive on MN seems way higher than IRL though.
I honestly don't think I know anyone over 25 or under 75 who can't drive. I know people who have a licence but can't afford to run a car, that's different, but no fully grown adult who actually can't drive.
At the younger end, lessons, cars and insurance are expensive, so that's understandable. At the older end, failing eyesight, reflexes, health and old age make driving difficult, stressful and frankly unsafe for some, especially in large cities (my DF for one).
For everyone else, driving's a life skill, like being able to swim, ride a bike, read and write. Sure, you CAN get by without, but it's a lot more difficult and restrictive if you can't - for commuting, just to even get many jobs, days out, holidays, shopping, to drop off and pick up kids/parents/friends etc...I don't know how people manage.
Public transport will get you so far, depending on where you live, but try getting a flat-pack chest of drawers home from IKEA home on the bus!!