Sadly, that's not been my experience. I can't say there's not a racial element; most likely there is.
I'm just saying being a white woman will not save you from being harassed by any man. I think it has a lot to do with location around areas of poverty or what I'm going to call drug lanes, homelessness, police presence and their behavior in areas they police, and access to goods and services or the overall callousness of the local merchants.
I live in a gated apartment complex but near an interstate, so there's a lot of drugs in the area. It's a poor, working class but not impoverished area. It's not uncommon to see police in the neighborhood but they harass men in the neighborhood for no cause who then turn around and harass women. There are a lot of homeless in the areas because they congregate around the on/off ramps. So, drugs and mental illness. This is a transient population. They come south to Phoenix and Tucson for the winter and head to Portland and Seattle in the summer.
I get harassed nearly every day. It's everything from inappropriate comments, to being hit on, to stalking or being followed, to raged at, to out and out threats of violence.
Two days ago the bus was behind schedule and the driver didn't see a man trying to get off. He had one of those trolley carts and was trying to stack his bags on top of it. Anyway, I had just gotten on and was coming down the aisle, when he called out for the doors to be opened back up so he could get off. I offered to help him lower his cart out and he just lost his damn shit all over the place. He started screaming profanities at me and asking if I thought he was crazy. Then he starts screaming about killing me.
He was a black man. I'm a white woman. Another white man and a Hispanic man laughed at this exchange and not nervous laughed. Entertained laughed. Another Hispanic man furrowed his brow, clearly uncomfortable, but turned away and closed his eyes. Another black man I've spoken with before stood up in case things turned ugly(-er). A teenage white boy told the driver to call security.
I get harassed by white men, black men , and Hispanic men every damn day. Being white is not some magic shield for me, though again, I recognize that might be different elsewhere. Probably is in a lot of places.
It's also true that of all the best men I have known, the best of the best... some have been Hispanic, some have been white, many have been black.