Anglo-Saxon in the sense of the article is principally referring to a political and cultural tradition that can be traced back to a certain place and time, the original dynamics of which continue to reverberate and resonate. Its association with any distinct ancestral ethnicities (i.e. something like "race") is in an important sense merely coincidental. Contemporary liberal politics is strongly essentialist in its discourse, so much so that people are starting to forget that such terms like Anglo-Saxon have alternative, more nuanced meanings (albeit not exclusively--there's
also a race-essentialist history, to be sure). The essence of identity politics is to fuse and fix, e.g., ethnicity and culture. It's why the American left assumed for decades that the growing demographics of minority groups with strong Democratic affinities would
naturally result in ever growing Democratic majorities. The notion that, e.g., Latinos would begin to adopt "white" social and political viewpoints with different historical roots was incomprehensible.
I think it's difficult to dispute that the principal political and social structures of the US, including California, are primarily derivative of the Anglo-Saxon model and its various facets, both in its core structures (e.g. how its democratic institutions function, economic life is organized, etc) but also in its relationship with oppositional groups (e.g. the Irish experience that continued to unfold in North America, and which also shaped how new groups assimilated into oppositional positions). This is most obvious in the context of our legal systems, but you can see it in both national and local political and social structures. Germans, Jews, Native Americans (to the extent they chose to engage), and everybody else assimilated into this system. They shaped it, to be sure, but the essential outlines remain distinctly identifiable as derivative of the Anglo-Saxon conquest of the British Isles going back to before William the Conquerer (most periods of which also involved clashes of culture and synthesis of foreign and domestic!). Could you persuasively argue that California politics is more like Mexican politics than it is the politics of other so-called Anglo-Saxon systems like the U.K., Ireland, Canada, Australia, or even South Africa? Also, don't forget that in most ways Californian politics is indistinguishable from that of Washington and Oregon, neither of which have strong Spanish or Mexican legacies that have persisted into the present day.
That said, I think the author overstates the explanatory power of Anglo-Saxon cultural heritage. It's impossible to understand contemporary American politics without understanding the contribution of mid 20th century French deconstructionists, or early 20th century Jewish intellectual immigrants, on both the left and right. Or even that of the American experience--when it comes to the prevalence of endemic societal violence, for example, North and South America altogether stand out distinctly from the rest of the world, for a multitude of reasons rooted in shared historical phenomena (e.g. slavery, frontier ethos, etc), few of which relate back in a distinctive, useful way to the particular history of the British Isles. Likewise, many countries, including Mexico, also saw similar French and Eastern European Jewish influences. And at this point there's an argument to made that it's more productive to set a new fixed point rooted in 19th and 20th century Western modernity, and US cultural hegemony that filters disparate influences as they take hold elsewhere in the world.