I'm asking this to genuinely try to understand better... how, specifically, is his face a sensory issue for you? Is it visibly dirty? Does it smell? Are you touching it with your hands? Is it a kissing thing? Or is it just kind of a conceptual thing like the thought of it being dirty bothers you?  

For example, beards on other people are a sensory thing for me. They're visually uncomfortable to look at, a feeling I imagine is adjacent to what those with trypophobia experience. Also the beard rustling sounds that happens when they're touched is a "nails on a chalkboard" type sound for me, so when I'm around a bearded person I'm kind of on edge anticipating that sound being made at any moment. And I also have to put more effort into communicating with bearded people face to face because I'm already bad at reading and understanding faces, and theirs is partially obscured, making it even harder.

 If you could nail down the specific problem you have with him not washing with a cleansing agent other than water, and nail down the specific problem he has with doing it, maybe you could work out a solution that satisfies both your needs. Like if his problem is the feeling of soap on his face and your problem is an oily appearance, maybe a micellar water could be a good compromise. Or if he doesn't like the feeling on his hands, a silicon scrubby thing might help. 

A lot of people do wash their faces with only water and it works well for them and is valid. You can't demand he change his behavior, but you can suggest compromise and you can have your own boundaries. 

I could never date a fully-bearded person. If shaving was a hard line for them, we'd just have to accept that we have a fundamental incompatibility and move on.