I say you have to have the right shoes for fishing. Most people wear their favorite tennis shoes and that is fine. Some fishermen wear running shoes, some wear sandals and some wear none I guess.
I have found that when I plan to be standing while fishing, something along the lines of a sneaker is good, but if you shop around a little you can find great shoes to wear while fishing that are functional. In a fishing shoe you want something that will remain sticky in wet conditions, will dry quickly if immersed in water and will not get stinky if you wear it wet.
I did some research and these are what I found. I can be found most days on the lake wearing my Keen sandals. Keen makes great shoes for outdoor purposes.