I work at home and don't drive much (3,000 km on the car). I have a 2017 Mazda CX5 I bought last fall. Most of the time it's in my (attached, insulated) garage. I drive it maybe once or twice a week. The other day I took it in and was told that the brake rotors are rusty and need replacement, and I should have my brakes serviced, too. Does this sound reasonable? I'm concerned mostly because if the brake rotors rust after one year, that suggests I'll have to replace them every year. The rotors are under warranty, doubt the brake servicing is.
Your rotors are likely NOT under warranty. They are considered "consumables" like windshield wiper blades and tires by every auto manufacturer I've dealt with. They may carry a manufacturers warranty (who manufactured the part, not the auto manufacturer. Tires are a common example).
As far as why are they are rusty, they are unpainted, untreated iron which rusts easily. Because they are thick, they generally don't have problems with rust, it's primarily surface rust. If the rotors are wet and/or cold when put away, they will rust. If they are stored in high humidity, they will rust. If you live in an area that uses salt on the road in the winter or the car is near a large body of salt water, that can cause rust.
Normal driving generally keeps this rust in check, buy scraping off the thin layer as it forms. In your situation you are giving the rust time to build up between uses. I'm not suggesting you drive more.
Questions: do they make noise and/or pull in one direction when applied? Are they causing any operational issues at all?
If you go out and brake hard 5 or 6 times you will likely scrub the rust off, assuming it's just surface rust.
If it were me, I'd laugh at the guy who suggested I replace my brakes because of surface rust. You might want to get a second opinion from another trusted shop.
Rusty enough to require replacing after a year? That's complete rot, total BS. Some surface rust is completely normal for an occasional use car. Some parts of the rotors will get rusty and stay that way because there's no friction to scrape it off, which is normal and nothing to worry about. If rotors are pitted due to rust I'd say definitely they need to go, however that takes a long time to develop and would not be a concern in your case.
There's no reason for a brake service either unless you are experiencing problems. the car's one year from new and hasn't been driven much, the fluid should still be fresh and the pads should still have loads of wear on them.
This sounds like an unscrupulous mechanic trying to squeeze money for unnecessary repairs. Report the jokers, and go somewhere else.