In my rowing days (actually the sixties of previous century), you had two systems in the boat: you had a "universal" system, where there were kind of straps with which you fasten your own shoes, and a more sophisticated one with shoes actually fastened to the so called "foot board". The problem is of course the size of the shoes. So, if a specific crew is the only user of a boat, you could have the shoes fixed on the foot board in the boat. If you have a boat that is used by many different crews you might prefer only straps.
Below an illustration.
By the way, also if you have fixed shoes you might use your own shoes to walk with the boat to the water, and leave your shoes either in the boat or on the quay. Some people might walk on their socks, but then you risk to get wet feet! But also if there are no fixed shoes, some rowers prefer rowing without shoes.
Therefore you may see rowers with and without shoes outside the boat, as you could see on the photograph of the Penn varsity crew team, 1914.

The vessel in the background, at about 3 o'clock, appears to be a ferry boat, the kind that carries automobiles...see the pilot house up high.

...they're wearing socks and no shoes because the shoes are in the boat. In crew you tie your feet right into shoes or shoe-like footholders that are built into the boat.

[Then why are the rowers in all the other crew photos wearing shoes? - Dave]