Too many of those shoes look like they have a munged Nike logo which means that any company trying to ship them would soon be receiving a kindly call from the Nike megacorp lawyers. You would have to improve the training to avoid generating trademark / logo infringing designs. Could this be trivially done?

In general this would not be easy.

One way this can be accomplished is by removing all shoes with such logos from the training data. But Nike and Adidas are disproportionally large parts of my training set, so this would not be feasible.

The other option would be to train a machine learning model to recognize said logo's and to use this model to remove sneakers with logo's from my generated images. This could however greatly reduce the variety of images on the website.

Slightly different implementation of your second option: Remove the logos in the dataset and train on this brand agnostic library

EDIT: To clarify - don't remove the entire image of a sneaker, just impute away the logo filling in the space with the 'context fill' algorithm found in photo editing tools

I don't think that is an issue: The process should just help the user find the right shoe. If the user repeatedly picks shoes with a logo, he will be presented shoes of that brand, that the vendor has in stock. This is actually beneficial to the trademark holder.

Only real shoes would be shipped...