The States can’t determine who qualifies to run for President.  The constitution alone states the criteria 
to be eligible.  If a Governor is idiotic enough to sign a law requiring a Presidential candidate to provide 
tax returns in order to be on the ballot, he/she would be a darling of the media until SCOTUS kicked him/her 
in the teeth.
Far lefty Jerry Brown (who didn’t release his returns  

 ) vetoed such a bill in 2017.  Newsom has Oval 
Office ambitions, so I don’t think he'd be willing to suffer a SCOTUS rebuke over the new bill currently 
floating in the CA legislature. 
“While I recognize the political attractiveness – even the merits – of getting President Trump’s tax returns, 
I worry about the political perils of individual states seeking to regulate presidential elections in this manner,” 
Brown wrote in a veto message. “First, it may not be constitutional. Second, it sets a ‘slippery slope’ precedent. 
Today we require tax returns, but what would be next? Five years of health records? A certified birth certificate? 
High school report cards? And will these requirements vary depending on which political party is in power?”
https://www.politico.com/story/2017/10/16/jerry-brown-trump-tax-returns-bill-243799