A quote from this linked paper:
Overall, we find that the combined federal and state tax codes substantially mitigate income inequality. However, state tax systems, on average, tend to increase income inequality slightly.
Washington state’s heavy reliance on sales and gas taxes—absent a state income tax—increases income inequality for Washingtonians. These taxes disproportionately affect lower-income households. By comparison, Oregon, which has an income tax but no sales tax, slightly mitigates (compresses) income distribution.
By the way, most of the overall compression of incomes results from the federal tax code. However, since at least 1980, the top marginal tax rate has declined dramatically, from 70 percent to less than 40. Meanwhile, income inequality continues to rise.