I would love to have someone change my mind here if I’m off base.
H1B visa holders pay state income taxes, sales taxes, and state disability insurance. They're considered residents for tax purposes at the federal and state levels which means they pay taxes on worldwide income, just like citizens and green card holders. Why should they be ineligible? That would be a repeat of SSI/Medicare, which they also pay but may never collect.
I'm perfectly well aware of the economic and tribal arguments. The former are not convincing and the proponents of the latter can go pound sand - given my preferences, I'd exclude them long before I'd exclude immigrants over paperwork.
There are people with family spanning generations on both sides and the border pretty much crossed them.
Here's a link to a NYT article about differing treatment in various states, with Cali generally lenient: https://www.nytimes.com/interactive/2015/03/30/us/laws-affec...