This one won't be easy to answer, since you are actually asking for a pH 7 soap, right?

I'd go down to a pool supply, or pharmacy and pick up a bottle of pH strips to test a few soaps.

Most soaps are basic (ie, pH higher than 7--usually closer to 9 or 10) because of the way soap works, chemically.

If I were looking to test a few, I'd try aquaphor or cetaphil first. They are very gentle cleansers usually recommended for people with babies with very dry/sensitive skin. Also, anything labeled as "tear-free" might be a candidate.

Do you have any marble you can do tests on?

You can use alcohol and water on both the marble and the mirror.

Are you looking for hand soap or a product for cleaning the marble?

For hand soap I've used a pH neutral one I found at Whole Foods. (Sorry can't remember the name off the top of my head.) I've seen a few others online and considered ordering. For marble vanity cleaner, I use Method (also from Whole Foods). One note, my significant other recently left a big blob of soap on the counter (without my noticing probably for a few days since this is a guest bathroom). When I saw it and went to clean it up, it left a shadow on the marble. I haven't tried any poltices to remove it, but just something to be aware of. Clean messes up quickly.

Thanks all. Kirk...Now that's way more involved ( ph 7,Pool stores etc) than I ever wanted to get for simple liquid hand soap. Have not seen Cetaphil hand soap. What happened with yours, prickly, is just what I'm trying to avoid. Hope it comes off, as I'm guessing it will. My granite will do that, but fades after a bit.
Marti
I had no idea finding ph balanced/ ph/neutral liquid hand soap,would prove so difficult.

EO Products! There was an earlier thread here that led me to them. They include both liquid and foaming hand soaps in their product line. I bought the foam at Whole Foods - they have an awesome range of fragrances, which are mild, pleasant, and quick to fade. Safe for marble, too. LOVE!!
Thanks for sharing the GlassPlus and alcohol/water references for glass; I've got a new marble vanity too!

Thanks Tina. Prickly mentioned whole foods too. Happily , one will be opening soon nearby. Those hand soaps sound perfect! Yea!!

Target carries Method granite and marble cleaner. I use it on my Calacatta Gold marble vanity top. I also looked for PH-neutral cleaners.

Many "natural" cleaners rely on citric and other acids to cut through grease. I accidentally sprayed Seventh Generation bathroom cleaner without thinking and it etched the counter terribly. Of course, it says right on the bottle "Do not use on marble."

I found this:

http://www.dianayvonne.com/category/11.thephofcommoncleanser/

So I checked and I've been using Kiss my Face hand soaps.

Kiss my Face Lavender & Chamomile Foaming Hand Soap

Kiss my Face Anjou Pear Moisture Hand Soap

I also put a glass dish under the soap dispenser to try to minimize drips and residue under the dispenser. I'm also wondering if the olive oil in the 2nd moisturizing soap I listed could have been what caused the dark spot on my marble. I'm considering switching back to the first (though the last time I was at Whole Foods they didn't have it). The dispenser wasn't great on the 1st foaming soap, which was why I switched to the other one. Anyone know if you can get an aftermarket dispenser for foaming soaps?

I also found this hand soap online that says "pH balanced" and have considered ordering it. But the price is so high, and they don't seem to sell refills (assuming the price is high because of the glass vessel).

Pure & Good Hand Soap @ Anthropologie

Good reason not to use marble for practical use like counter tops IMO. I have been trying to find out which if any dish detergents are PH neutral to use on my new vinyl floor. They sell a ridiculously expensive cleaner where I bought the flooring ($30 a bottle!). I read a little bit of dish detergent in a bucket of water would work, but I want to be sure.

I just called the Colgate/Palmolive co and was told the PH is between 6&8 so it should be fine. Wonder why they don't put it on the label. 12 1/2 ounces for $1 at the Dollar Store. A whole lot more reasonable than Whole Foods etc.!

This link maybe helpful http://www.helloprettybird.com/2015/09/low-ph-body-wash-reviews.html