I have a safe deposit box at our bank where I keep a computer backup drive and our passports. I backup to a local external drive nightly, then swap that drive with the one in our safe deposit box about once a month.
Remember, there are more risks than fire, including floods, tornado, hurricanes, theft, landslides, etc. In the case of a backup drive, the drive itself can fail even if you don't encounter a major disaster. Multiple backups in multiple locations is key.
I do have a small fire safe here at home too. We keep things like our wedding certificate, death certificates, home records, etc. in it. Important papers for sure, but nothing that couldn't be replaced if needed. Whenever possible, I scan and digitize these papers so I have a digital copy I can backup regularly.
The home fire safe is only rated for one hour, so it certainly wouldn't survive a forest fire if we weren't here to take the safe before the fire got here. It's also not rated for media. It may prevent paper from burning, but flash drives or optical discs don't stand a chance. They do make media fire safes, but you're still vulnerable to the situations listed above.
These days I try to have a digital version of every document possible. That's all of our bills, property tax statements, birth/death/wedding certificates, etc. Once it's in digital form, I have a copy on my computer, two backup drives (each in a different location), and the most important documents get burned to a BluRay data disc as another layer of protection.