You can certainly do business with companies, while showing preference for an organization that shares your values whenever such an organization exists.
but thinking Mozilla values privacy because it is a non profit is not a great reason.
I think it is more that some people (including me) think Mozilla values privacy because they flat out say they do and then they have a consistent track record of supporting privacy. The fact they are non-profit does make it slightly easier to take their statements at face value, but it is their track record that really demonstrates it.
Mozilla's entire business model isn't based around getting to know you or you habits better. Google has an inherent and fundamental financial interest in being able to follow what you do browsing day to day.