None of that is unique to California. Your overall tax burden in California will be about one percent higher than Texas, according to https://wallethub.com/edu/states-with-highest-lowest-tax-bur..., though Californians typically lay spot more taxes because they make more money.
In general, people put ~5% of their (pretax) money into 401ks because, on average, companies will match that ~5%, effectively doubling your retirement savings instantly.
A common thing to utilize after that is a ROTH IRA, which is paid with after tax money, but the money grows tax free. The max ROTH IRA contribution per year is $6k, $12k if you're married.
Tax-exempt would be never paying tax on it.
He should have tenure. The UC system doesn’t pay that great, and there is also a lot of competition for faculty positions. Your best bet is to make some money on the side , legally of course, advising some company, but even that has a lot of restrictions.
Those aren’t low rates compared to other states, especially considering the COL.
I think you are either too optimistic in what a professor can earn in California, or you are missing that taxes are marginal. I know a CS professor at UCLA who just makes around $120k, so single filer California taxes would pay just be around 6.5%. If you throw in a spouse with an additional $80k of income, you’ll hit 6%.
To pay an effective 10% rate in California, a single filer would have to make $700k/year and a married couple would need to make more than a million.
A school like UCLA deals with their faculty not making enough to buy a house in LA (or especially Westwood) by giving them access to special kinds of loans.