No, they do not have to be consistent.

In my kitchen I have stainless faucets, but all bathrooms are different.

You can even mix metals as long as they go together with the overall vision [like different sink faucet than shower faucet; light fixtures, etc.]

Do a 'vision board' for each room.

No, they do not have to be consistent. That's OCD.

When we pick hardware finishes, is it usually recommended that faucet finishes be consistent throughout the house (kitchen and bathrooms)?

Why and who recommends that?