I practice in workout gear, but am generally in practicewear and heels for lessons. On rare occasions - think injury - I might be in practice shoes and black pants. I feel like dressing up a little shows respect to pro/coach, and shows that I take this seriously. Nothing elaborate, but I have a few skirts that I rotate, and a collection of leotards/black t-shirts.
There is a pro that I often see who will teach (solo students or couples) in jeans and flat dance sneakers... and I just find it disrespectful, like they are telling the student that they're not really planning to work all that hard. Seriously, it takes 2 seconds to throw on a pair of dance pants/skirt and some shoes - practice ones are cool with me, as are the dance sneakers if you are injured. Plus, if you won't let the students you are teaching wear jeans (the studio has a dress code for kids and teens), then you probably shouldn't either.
When it comes to students, I'm more open on wardrobe choice. Wear what you can afford and lets you move, preferably not too skimpy. Wear a version of the same outfit every day if you like, or never repeat. Don't care.