I don't think you understand Simpson's paradox.
It is Simpson's paradox that makes it appear that poor people vote Republican and rich people vote Democrat, when the reverse is true. That comes from ignoring the other variables that are implicitly included when you subset by state.
Your final paragraph agrees with my claim: richer people tend to vote Republican, poorer people tend to vote Democrat. That's what I said originally.
The interesting fact is at the state level: Republicans living in blue states tend to be richer than Republicans living in red states (just as everyone else in blue states tends to be richer than in red states). If you were a Democrat, you'd attribute this to the success of Democrat policies. If you're a Republican, you say that they are rich in blue states because of the Republicans, despite all those Democrat voters.