Can wearing padded cycling shorts versus regular shorts affect the adjustments during a bike fit?
You should go for a fitting in whatever clothes you'll be riding the bike in. Any fit system that doesn't let that happen is being misapplied at best. Clothes can affect your range of motion, preferred position, and effective body dimensions (more in the case of shoes than this), etc, sometimes in ways that are subtle or unforeseen.

I don't have anything necessarily bad to say about Retul in regard to the kind of riding it's really meant for (race/performance), but a professional fitter should be the first to tell you to come wearing your actual riding clothes. That's foundational, especially if a client is doing more utilitarian or casual riding that's outside the racer mold. You're experiencing the wrong end of the difference between using a fit system as a tool, not a crutch. Get a different fitter.