But they're with a group of like-minded people whose rules reinforce many of their other NIMBY tendencies (i.e. no homeless shelters, adult bookstores, garish homes.) They agree with most of the rules, but because they want more control they tend to complain loudly about the ones they don't like.

HOA boards are democratically elected.

They make their own rules and voting laws. There is no requirement of equal representation like the US Constitution provides.

Does every member of a family get a vote? How about every adult? Or is it just one vote per household?

The US constitution is but one of many sort-of democratic frameworks. And not overly democratic in its consequences (see gerrymandering, and the effects of the electoral college, or just all the problems with first-past-the-post even in theory).

So while HOAs have their obvious deficiencies, your attack is one of the weakest complaints imaginable.