I don't know what your monthly spend is, but there are income levels where you'll see 0% capital gains at both the state and federal level. Also remember that you'll only pay the tax on the _gains_ (ie, taking your cost basis into account).
Moving out of a state for avoid a low-single-digit tax on _gains only_ seems like it may be an over-optimization, but you'll have to look at your specific situation.
RSUs are taxable on vesting, and California wants its piece of that, if any of the vesting happened while you were a resident or working in California. But after they vest, they're just stock, and when you sell stock, California considers the capital gains to be sourced to your state of domicile.
If the OP was being loose with terminology, and the 'RSUs' to sell already vested, there's no California tax due on sale if they've moved out of state before the sale.
Yes you assumed right it is for tax reasons. I have some RSUs and other stocks that I could sell and only worry about the 15% federal.