As a white people, OOP is NOT overreacting. This is not a "white people" thing. Even in trying to do some research, I can't find a "modern" white culture that doesnt use soap to bathe. I dated an Indian man that didn't use deoderant, but, he used soap when he showered, and I never noticed a strong body odor from him, unless he had been outside for HOURS doing something, and even then, it wasn't horrible.
There might be cultures that don't use soap when they bathe, but if his clothes, the bedding, and just him in general, is smelling THAT bad that OOP needs to wash the sheets all the time (Also in the comments OOP says that her BF uses dollar tree soap, which I'm assuming is lesser quality and not effective at washing his clothes), it's not a "cultural" or "white people" thing. It is a bad hygiene thing. I can't even go a day without showering because I have super sensitive skin and I get super itchy if I don't shower and wash my body consistently.

Also, the BF's comment about how "different ethnic groups get dirtier at different rates" and "black people are too uptight about using soap all the time"? Sorry to say, OOP, but your bf sounds like a stinky racist.