TLTR: Got Turned Down for a Job Interview for Not Wearing Dress Shoes

I'm trying to find a job and a company that isn't related to my field called me and said "we looked at your resume and you seem well fit for our open position." I didn't apply here, they called me(I've given my resume to staffing companies), and they setup a interview with me 5 days later(which was today). I went there in rush hour traffic (annoying 30-40 min drive) arrived there, checked in, and waited in the waiting room. I was then greet by the company's manager who said we cant do a interview with you today because you're wearing sneakers. I told him I understand the job requires you to wear dress shows and business attire, but this is just a interview, a QnA about my Education, experience, and more. What does my attire have to do with what I can bring to the company. And he said the classic "Dress to Impress" line. I don't know how many other people they might have done this to, and if they did they definitely missed out on some talent. Again I probably wasn't gonna get the job anyway since I know Im not the best fit for the job, but HEAR A DUDE OUT FIRST before you say something like this. They could've easily done the interview and then warned me at the end about the shoes and dress code, but they aint even let me have a chance to speak. Nobody in there was rude or mean, they were very polite but I'm just mad, I went that far for a job I'm not that interested it, and then they added insult to injury. I've learned 2 things from this

1. I will be wear FULL proper attire
2. I will not go to job interviews that aren't in my field

Edit: Too many comments to respond to. So I will address them as a whole. Thank you all for taking your time to comment on this post. I welcomed all the tips and critical feedback I received from everyone here. I know I messed up, and as some of you called it, I made a "rookie mistake." Thanks to everyone, from lifeguards to nurse and hiring managers themselves to IT pros, thanks yall. Hopefully all my other interviews in the future go wayyyyyyy smoother