If I image a USB flash drive with an ISO, does the filesystem (FAT32, NTFS, APFS, ext4, etc) that it was originally formatted with matter? Or, does the imaging process somehow eliminate and irrespective of the filesystem type?

In other words, if I create a bootable USB flash drive by imaging it with an ISO, can I ignore how the flash drive was originally formatted and can I then boot to that flash drive on any device (macOS, Linux, Win)?

The system still has to be able to read the original data format or it will not even recognize the drive or the ISO stored on it. Once you boot into the ISO, that virtual system will act as if its whatever file system you put on it.

Yes. The current filesystem on the usb drive is irrelevant. The iso image is a bit-for-bit copy which includes a filesystem. Assuming the iso is a bootable image and not just a partition, just image the usb drive. Make sure usb boot is enabled in the BIOS/UEF on the PC, Mac, etc, and you should be go to go.