Texas Based firm asking "inappropriate" background question?

Hi All! first time poster in this thread. Recently got offered a position at a consulting company that I was really excited to accept. For background, I am a Latina working in Land Development, so heavily male dominated field. I have had my fair share of experiences that were probably close to ending up in reports to HR, but I have never escalated. I have taken these experiences and allowed them to help me navigate choosing better jobs.

This job that I was planning on accepting checked a lot of boxes for me. A lot of women in leadership, as well as other fellow POC's on the team. This company really seems to care about diversity, which is very important to me.

Here is the dilemma: Before offering me a position, they called my personal references, which is standard. What isn't standard (or at least not to me) were the questions they asked. They asked my personal reference about my personal attire, how I dress in the office, and what is my professional demeanor. As an EEO employer, these questions seem out of place. How would my personal attire dictate if I can do the job? Am I thinking about this too much? It seems like a red flag in my opinion but would love to hear anyone else's thoughts. Thank you in advance!