https://www.houzz.com/discussions/do-all-fixture-finishes-need-to-match-in-dsvw-vd~31219
Varied opinions...

I do believe in a very cool, spa like bathroom all the finishes should be the same. It creates the gentle tranquility that is commanded in this arena. But, if you are looking for a more traditional look, the Victorians combined everything in the 19th century and so you can mix as they did.

I was trained under the beliefe that all finishes in a room should match. However, tastes have changes, and as women do not wear matching sweater sets any more, designers do not match all finishes in a room. However, do not be fooled into thinking these are random choices. A good designer scrupulously weighs the benefits of various elements to come up with a harmonious result.

Great design is created when your eyes flow smoothly around a room without too many stopping points. I'd keep all the hardware the same.

I'm thinking these *do* match, I see gold and silver mixed on all of the fixtures and towel bar. So, this example is not exactly the same as mixing entirely different finishes. Some earrings and other jewelry are gold & silver mix today. Unless you're an expert as Turner describes, better to stick to one finish or the other unless you like that patched look.

If you are doing it yourself, I'd recommend matching. It's very tricky to match finishes and get the right balance - most designers know how to make this look right and if you are working with a professional, trust them and be open minded. Otherwise, probably better safe than sorry.

Love the mix of finishes! I've read conflicting views, but personally love to mix them up.