@Think first
This woman was so impressed with his commitment to his religion that she did the business deal with him.
I am reminded of when NYT ran a column a number of years ago (don’t know if they still do) called The Ethicist (IIRC) and there was a huge raging discussion about a situation where a woman wanted to “tear up a contract” because the frum guy who she signed it with wouldn’t shake her hand, and she was offended. (Tearing up the contract, btw, would not help her AFAIK – once you sign, you’ve signed.)
I do not shake hands. But people will sometimes be respectful, and sometimes not. You can help by being respectful and menschlich about everything yourself, but it’s not all in your hands (ouch!).
This incident sounds apocryphal but is so common it actually happened to me – when I explained that I wouldn’t shake hands for religious reasons, someone said, “Oh, so you’re shomer negiah?” I found it amusing that I was looking for ways to phrase it just right and they had smoothly figured it out already.