I'm not a dive pro, but have been a student on more than one occasion.
Ultimately, it's up to the shop. If they require you to wear similar gear, then you have your answer. If not, I'd recommend you don't change.
It's useful to have new students gain at least some familiarity with different gear style. Better to see it for the first time in a class than on an instabuddy. Over the past several years, I've taken a few courses, and went along when my daughters' got certified. My gear is similar to theirs (Back-inflate, combo inflator) and they used their gear during their classes. The other students were all in shop rentals (jackets, standard inflator, standard octo). I appreciated that the instructor took the time to point out the differences.
When I took a rescue course, between the instructors and my fellow students we had most gear configurations covered. No jacket BC, but everything else. There was a mix of back-inflates and backplate and wing, standard octo stowed, combo octo-inflator, and necklaced octo. It was on us to be familiar with each different configuration.