I think it's a reasonable ask. I don't think many of us purposely douse ourselves in perfume and such prior to a date because we're conscious that you're potentially going home to a partner/ family, or may have allergies. However, shampoos, body lotion, the like, also have strong smells, so it's always best to just ask the provider up front if they wouldn't mind coming scent free, if that's your preference, to your date
This is a problem for me too. If I'm going home right after the date I bring a garbage/recycling bag with me to put my clothes in (some room scents can really get into your clothes), I also bring a travel-size version of my body wash to the appointment. All this is on top of asking for no scent, but sometimes it can't be fully mitigated.