Noncitizens aren’t totally barred from voting in San Francisco. In 2016, after multiple attempts in previous years to pass a similar measure, voters approved Proposition N, which allowed San Francisco noncitizens to vote in school board elections if they had a child who went to school in the district.
What's wrong with voting in school board elections?
So, I know where you're coming from because I've read stuff by Edmund Burke and other conservatives. But, unless the conservative you're talking with is the intellectual type, they probably haven't. They've probably just internalized some version of social conservatism but would also be appalled that you'd accuse them of supporting social stratification even as they support it.
I learned some time ago that this particular argumentative strategy is incredibly pointless. They don't care that you know the historical and philosophical foundation of their beliefs. For them, that foundation isn't there for them. They probably don't know it! Their life experiences inform them more than anything else.