A brief commentary, not a review.
Andrew Gelman's book has a good deal of useful information. Neglecting some important questions reduces its value.
There is a reminder that all states are purple, and even in states we think of strongly one way or another, it's a 60-40 split. This isn't new - in fact, it should be obvious to anyone who stops and thinks about it a few minutes - but it can't be said often enough. We like our data packed into economical packets, so we are attracted to the largest simplifications we still find satisfying, but these mislead. One of the most intelligent people I know commented with rolled eyes about a trip to Tennessee, and what an obviously red state it was, with its guns, confederate flags, churches with big message signboards, and pro-America bumper stickers. Problem is, Tennessee isn't that red - and she was in the bluest section of it. Good chance those were Democrats in those pickups.
Of considerable interest in thinking about voting preferences and relative, rather than absolute wealth, Gelman notes that the richest states tend to vote Democratic, but the wealthier voters within each state tend to vote Republican. Similarly, in the blue states the poor have higher church attendance - in red states, the wealthier attend. That's a bit more nuanced, a little less predictable, than we are used to describing. These sorts of odd breakdowns, not shocking but not quite what we thought, make up the bulk of the book. If you like that sort of thing, Gelman's got plenty.
Two things left me mistrusting some of his conclusions. He does not break down the voting patterns of the poor into black and nonblack (or white and nonwhite, if you prefer). I get that he is trying to show voting tendencies in terms of purely economic considerations, and racial data would be a complicating factor. But it is likely an important complicating factor. Remember that these voting tendencies are much like the purple states. If 60% of a group votes a certain way that is comparatively significant because in the American context, that's a big split. (Compare to say, Romania, where the UMDR receives almost no votes from ethnic Romanians - it's a Hungarian party.) If African-Americans are disproportionately represented among the poor, and they vote 90% Democratic, that can create a false picture that some trends are economic when they are in fact racial. Perhaps the tendencies Gelman reports hold up even if this adjustment is made, but they would at minimum be far less robust.
Secondly, the Democratic Party is a coalition of groups, far more so than the Republican Party. Thus, popular generalizations about Democratic voters which Gelman debunks might in fact be strongly true about one or more members of the coalition. He is at pains to illustrate that stereotypes about Democrats as wealthy latte-drinking liberals are not true. I believe the numbers he puts before us, showing that Democrats do not dominate among the wealthy, are true. But the Pew research category of liberals, which makes up 19% of the US (and therefore well more than a third of the Democratic Party) are indeed much wealthier than the other groups. I don't have the data on latte, but the stereotype he purports to debunk is in fact true - but only for a large but definable portion of Democrats, not the party as a whole.
Just for sake of guessing, Gelman's misunderstanding of some conservative ideas tells me he is not one. He does not come off as especially liberal, however, and may be an honest broker - a commodity in short supply these days.