There have been very few companies I worked for where I "believed in" what they did in the sense of thinking they were doing something amazing and world-changing. But I "believed in" them enough to know they were doing things I found interesting and could afford to pay me.
> I can't be productive and efficient working on stuff I despise.
There's a huge amount of space between believing in something and despising that thing.
> It's like trying to swim while being skeptical about touching water.
I think being nervous about touching water when trying to swim for the first time is healthy and rational, and may even make your ultimate success more likely. I'd be much more comfortable working with a founder that had a healthy amount of skepticism than a founder who was a "true believer".
I suspect I'm purely getting trip up on language here, though, and I probably agree with your underlying sentiment.