Everyone can join a credit union, but not everyone can join any credit union.

This turns out to be a source of much confusion for consumers looking for a better checking account, a more generous credit card or a cheaper auto or home loan. By their very name, credit unions suggest exclusivity. After all, unions are something you have to join, and it isn’t always clear from walking by a credit union or running across one on the Web whether everyone is welcome.

But over the years, some of the biggest credit unions with some of the best deals have quietly opened up membership to everybody. This infuriates bankers, who must compete with them while also paying income taxes that the nonprofit credit unions do not owe. Consumers, however, ought to rejoice and take a closer look at some of the more aggressive credit unions, since there may be big savings for the taking once you realize you are eligible.

Bankers’ irritation is rooted in part in history and their contention that many of today’s credit unions barely resemble the institutions of old.

Credit unions got that tax break early on, when they formed to serve customers the banks wouldn’t touch (the “small people” in BP speak).