I have a two-disk NAS in RAID 1 that's not cooperating. I tried taking one of the disks out and plugging it into my iMac via a USB enclosure to copy the files off of it, but MacOS can't read the disk. I assume it's probably Ext3 or Ext4, some kind of Linux format. How can I get the files off of the disk?
Linux is very flexible when it comes to filesystem formats and disk setups.
The most common problem you will encounter is the most popular filesystem for Linux: ext4, which is of course not supported by Apple under macOS.
A great many more exotic filesystem setups cannnot be dealt with from within macOS.
A more convoluted but more flexible solution method might involve either booting your Mac into Linux and copy the files or using a Virtual Machine that runs Linux to extcrat the files.
Virtual Box usually can handle USB (provided the settings are right) and most Linux installations from within there as well (again: settings). The Linux installation needs support for the actual filesystem (mainstream distributions usually do.) As the RAID was 1 aka mirroring, one of the disks should then be readable.