It really depends on what one considers being "normal clothes".
I wear a uniform at work, we get food/drink splattered within half an hour of starting work.
I will normally cycle in a pair (or 2 if baltic) of leggings, top according to the temperature, a beanie hat, a buff for the neck only, grippy shoes again according to the weather: commute is 5 miles each way.
If it drizzles, I let my legs get wet, I don't mind, change at work anyway.
If it rains heavy I'll put a waterproof trousers on.
In winter I always wear my
Altura night vision jacket because it keeps me dry and not too hot.
If it's mild and dry, I might put the jacket in my panniers, as it could rain any minute here!
Since starting using the bike as transport, I had to give up wearing my woolly jumpers and would really only cycle in jeans if there's no chance of rain, as they feel horrid wet.
Today was cold but dry, cycled to work in lycra (not cycling) leggings plus a pair of warmer ones.
Had a long sleeved polo neck on, and a short sleeve top.
Merino socks and walking shoes, plus my cycling jacket and my hat.
Because I was not working with the public today, I just kept these clothes on for the shift.
In summer I would wear leggings with a dress or seamless trousers and a vaguely sporty top.
I tend to buy my clothes with a view of how comfortable they would be on the bike.
I hate padded shorts, and the polyester cycling tops are made of, the ones I have tried anyway, smell funny imo.