The building’s board (generally not all residents) voting on whether you can buy is true for NYC, at least for most co-op buildings. Generally not condos. Criteria vary from “basically financially solvent – i.e. 10% down and 2 years PITI in the bank” to the absurd, the latter being much more rare.
However, the basic process actually makes a lot of sense — it keeps the jokers who want to buy with 105% financing out of the game. This has kept the foreclosure rate in Manhattan very close to zero. It’s a matter of self-protection rather than snobbism, since insolvency of a co-op board could potentially result in foreclosure of the entire building.
BTW, imagine if condo boards and HOAs in CA would have been able to reject buyers based on crazy financing methods back in 2005 – a lot fewer people may have been burned.