Playing the organ in street shoes is acceptable under certain conditions, as long as the shoes are specially made, of the right construct, and made of the right materials [See blog, Balance in Organ Playing, Part I].
These are important to get and to wear, each and every time we perform, each and every time we practice [See blog, The Ten Commandments Of Organ Practice].
Few shoes are designed specifically for organ playing, but probably the best known in the USA are made by the Connecticut based company Organmaster.
Organmaster shoes (photo) are made by Capezio, though they differ somewhat from the dance shoes this company sells [See blog, Shoes, Part IV]; the soles, for example, are very thin for "feeling" the pedals through the shoes, which makes them vulnerable to wear if the player would decide to use them for street shoes; they almost need to be left by the console and changed for street shoes when the organist leaves; for all of their advantages for playing the pedal keys, they make a very poor street shoe.
The typical features of an organ shoe are 1) a flexible, lightweight leather or synthetic upper held snugly to the foot by a lace, strap, or ribbon; the material should allow the player's feet to glide against each other without sticking together, 2) a soft, flexible leather or suede sole that allows the player to slip the foot easily both up and down a pedal and across pedals; the sole should be thin enough to feel the pedals easily, and it should not extend beyond the sole of the foot, and 3) a slight heel of about an inch in height, wide enough so that it cannot become wedged between 2 pedals.
There's an additional consideration: Some performers prefer to leave their organ shoes by the console and change into them from their street shoes each and every time they practice or perform; others prefer a dance shoe that they can wear into and out of the building, as well as for playing the pedals; if the player can manage to keep dirt and grime off the pedal keys by wearing only one pair of shoes, then this would seem more sensible, rather than having to keep track of a shoe box and carry it around with them all the time.
Many types of footwear, however, are completely unsuitable for pedaling; these include sneakers and other rubber soled shoes, flip flops, clogs and any other shoe that fails to hug the heel, platform shoes, "chunky shoes," or any other heavy or inflexible shoes that would slow or decrease the agility of the feet [See blog, A Third Hand].
(con't in Part II)