Your claim is dubious. People don't balk because of closed-source. They balk because they don't know whether your SaaS is worth relinquishing their personal data.

Until we know what it is your SaaS does, it's impossible to advise on open sourcing. Generally, however, unless you've patented an algo, always open source. For the last 15 years, code is cheap commodity, and getting cheaper. The only companies capable of sustaining a proprietary model are big and old, which is not you. You will need to feed yourself from high-touch service level agreements.