Are they uncomfortable with you accessing their data, or are they uncomfortable with you storing their data unencrypted, risking their IP in case of a breach? Two different things.
The former means they aren't a fit for SaaS (i.e. offer self-hosting), and the latter means you can use at-work encryption, only decrypting the data to process it.
Without more info on what you're actually building, I can't really be of more help here.