The rates are extremely similar once you control for race (which the page you linked allows you to do, by the way). White people get skin cancer at much higher rates than non-white people, because melanin acts as permanent mild SPF, and white people have less skin melanin than non-white people: that's what makes them white, after all. Since Washington is more white than Hawaii, California, and Texas, if you don't control for race it looks — counterintuitively — like Washington is more risky than the others in terms of skin cancer. But it's not, it's just that you're selecting different population demographics.

Also notable is that sunniness doesn't really determine UV exposure; partial cloud cover can actually result in more UV-B exposure, counterintuitively: https://www.drgurgen.com/are-the-suns-uv-rays-really-stronge... And even full cloud cover doesn't completely block UV. So WA and CA aren't as different as you might think.

Meanwhile, as one might expect, most states that get freezing cold for months at a time have lower skin cancer rates than those that don't when controlling for race: if you don't go outside for more than a few minutes a day, while bundled up under multiple layers, for months at a time, well — you see less skin cancer. Some heavy farming states seem to have more skin cancer, but again that makes sense since farm workers are outside a lot.

Vermont and New Hampshire seem like odd exceptions to this rule — but I suspect there's also just some other selection bias at play. UV exposure from the sun causes skin cancer at high rates in white people; trying to make assumptions about states isn't necessarily an easy thing to do, since many other factors are at play when considering who lives where and how much they go outside.