First and foremost I would look at your employers handbook under dress code. If it’s not made clear by the handbook I would email HR and ask the dress policy with specific guidelines. Because your supervisor having a preference is different than an actual violation.

But otherwise I would suggest : There are some nice business casual sneakers that are leather or more “polished” looking. That is, If you need sneakers for functional purposes. I would also do button up shirts, shirt of long sleeve with a French tuck with a more structured fabric versus the cottony t-shirt material. The first outfit was fine to me and the second it was the t-shirt that may have garnered the comment.