By that argument dry-cleaners should have already been open this whole time, except for the part where nobody was going to work. But liquor stores, coffee shops (that don't really serve food), auto detail shops (to name just a few things in my neighborhood) have been. Along with bike repair shops and my local UPS Store, both of which can be necessary services.
Realizing that every state has been different. But categorizing types of permitted businesses is an inevitable part of this process, even if there seems like common sense ways (based on the number of people/interaction involved) to do it that are otherwise neutral.
In Texas the category is simply "retail," and they have to stay at 25% capacity (and can also keep offering pick-up). Dry-cleaners would be included in that I think, even though they sell a service rather than goods. Malls also included. Should the corner store or a dry-cleaner be subject to the same standard as a Dick's Sporting Goods? I dunno, you could argue about that in either direction (i.e. a 25% full Dick's is roomy but being with just 3 people in dry cleaning line if their legal capacity is 12 might not feel comfortable).
Barbershops, gyms, hair salons are a separate category and still three weeks out in Texas.
It is funny how different anyone's experience is depending on where you live, i.e. Ross mentioned "drive-thru windows" at the dry cleaners which is not something any dry cleaner within 5 miles of me (in downtown Portland) or any dry-cleaner I've ever been to in Manhattan would have, though of course I've used them in other places. Laundromats would be something else entirely. In our own apartment building we have four washer-dryers so 25% capacity - as far as an actual person being in there - sounds perfect to me (unfortunately not everyone in our building seems to agree).