Don’t really care what anyone else thinks, but do have a self-respect issue with details such as what shoes and pedals etc… I prefer mtb (recessed) cleats and boring old Shimano touring/mtb leisure shoes. I don’t think they look wrong, particularly on my road bike, which is Audax/light tour/winter trainer style. I ride to work (12.5 miles) and just wear the cycle shoes with jeans at work – they’re kinda brown and black suede, and quite inconspicuous.
For a proper racer road bike I think I would feel obliged to get some proper road shoes – but that’s not a great bike for just riding about anyway…
As for flat pedals on a raod bike – well, a Dutch shopper or any old pub bike would be fine, but anything with drop bars deserves clipping-in. If the bike is sufficiently old, toe straps would be perfectly acceptable, ableit with the correct shoes!