I list everything that goes into my soap, including sodium hydroxide. I also educate my customers on what it is, and how amazing it is.
And the few customers that have said "oh, so and so's soap doesn't use lye, she told me so."? I encourage them to research for themselves and discover that oh, yes it does. And her customers are now my customers - her soap may be great, but once the lie is discovered, all credibility is lost. This wasn't my intention at all, but it's kinda karmic anyway - she lied to her customers' faces and told them she used no lye, I can't save you when you hang yourself with your own rope, KWIM? (And no, not a negative word passed my lips. That is not who I am as a business owner.)
So much of our businesses and our brands are built on customer confidence. If the customer feels you aren't confident enough in the safety of your product to list its actual ingredients, they'll go elsewhere. Maybe not right away, but I have found that handmade soap patrons are passionately interested in trying and learning new things. And eventually, the "lie by omission" is discovered. To me, that is not worth it.