"Can we use Webb’s telescope shield to prevent or significantly reduce boil off of propellant from StarsShip fuel depot in Earth orbit?"
Yes we could. However the JWST required very low temperatures in order to ensure its highly sensitive instruments worked properly. It would not be necessary to cool Starship to the same degree so using the JWST shield would be very expensive and unnecessary.
"what size shield do we need to have?"
It really depends on to what extent you want to reduce the boil off and how reflective it is. It would be best to shield the whole vehicle to prevent conduction through the skin from the cargo bay area down to the propellant tanks. It would be most important to shield Starship from the Sun, but shielding from Earth light would also be very beneficial.
"By what principle would it cool the cryogenic fuels?"
The shield would firstly prevent radiation from the Sun and Earth being absorbed by the tanks and warming them up. With sufficient shielding the tanks would lose energy by radiation. In the most extreme case, if Starship was 100% shielded from everything except deep space Starship would slowly cool down to the background temperature of space of just under 3 degrees K.
However this process would take a long time due to the mass of Starship and the fact that the contents of the tanks are liquid. The cooled liquids would slowly freeze but this would also involve removing the latent heat of fusion and radiating that away to. But given sufficient time the contents would freeze completely solid and tend towards around 3 degrees K.