I'm assuming you are a gentleman, from reading your message. lol I am sure that they will not turn you away if you are wearing a cleaning respectable outfit. We went last year and my finace' wore flip flops with his nice khakis and button down shirt and he was fine. No one really stares are your feet. Use your discretion i would say. HOpe that helps.
I can tell you that men can/will be turned away at Feathers if you arrive in "flip flops" or open toed sandals. Any type of closed toe shoe is acceptable. My husband has also been allowed to wear leather sandals that have a closed toe and a strap around the heel area.
Take my advice - don't show up in inappropriate foot wear. You will not be seated.
The service and the food at Feathers is outstanding,I am a shorts and T-shirt guy but wearing slacks,a button down light weight collared shirt and dress shoes was not a big deal and it made the evening meal a bit special. The restaurant is nicely air conditioned so comfort was not an issue either.
I'm going with the chucks ... with some emergency dress shoes in the suitcase as well.
To set the record straight, I'm not a black jean cut-offs, tazmanian devil tank-top and grass-stained sneakers kind of guy. I can present myself appropriately. But, when possible, I prefer to complete my outfit with a pair of sneakers, as opposed to dress shoes.
Trust me, my wife (who uses this screen name as well) often ridicules me for both my neuroses about dressing properly and my passion for sneakers.
I just prefer to be "properly dressed" my own way. That will fly some places ... others, not so much.