Step by step Procedure

Following the Arch Linux Raspberry Pi 3 Installation Guide, it is possible to abstract the steps necessary to do this on macOS without any virtualization. It is a matter of understanding what is going on and knowing macOS tools (which are just enough different than GNU tools be be a pain).

A quick look at which filesystems are necessary: mkfs.vfat is just mkfs.fat, which can be FAT12, FAT16, or FAT32.

diskutil listFilesystems
-------------------------------------------------------------------------------
PERSONALITY                     USER VISIBLE NAME
-------------------------------------------------------------------------------
Case-sensitive APFS             APFS (Case-sensitive)
  (or) APFSX
APFS                            APFS
  (or) APFSI
ExFAT                           ExFAT
Free Space                      Freier Speicherplatz
  (or) FREE
MS-DOS                          MS-DOS (FAT)
MS-DOS FAT12                    MS-DOS (FAT12)
MS-DOS FAT16                    MS-DOS (FAT16)
MS-DOS FAT32                    MS-DOS (FAT32)
  (or) FAT32
HFS+                            Mac OS Extended
Case-sensitive HFS+             Mac OS Extended (Case-sensitive)
  (or) HFSX
Case-sensitive Journaled HFS+   Mac OS Extended (Case-sensitive, Journaled)
  (or) JHFSX
Journaled HFS+                  Mac OS Extended (Journaled)
  (or) JHFS+
ZFS                             ZFS Dataset

Indicates that MS-DOS FAT 32 is supported.

Find my SD Card.

diskutil list
... 
(internal)
...
/dev/disk2 (external, physical):
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:                                                   *64.1 GB    disk2

Apply FAT 32 Filesystem to my sd card like in step 3 of the guide. The diskutil help does not make it obvious how to run something like mkfs.vfat. diskutil partitionDisk -h is somewhat useful.

                      #/dev/node  PARTSCHEME FS LABEL SIZE (R=remainder, 100%)
diskutil partitionDisk /dev/disk2 MBR FAT32 BOOT 100M FAT32 ROOT R

(replace disk2 with the device node of your sd card)

macOS will automount the new partition at /Volumes/PI, so skip the mount step.

Extract ArchLinuxARM-rpi-3-latest.tar.gz directly to the mount point. MacOS is closely related to BSD, so tar on macOS is bsdtar.

tar -xvf ArchLinuxARM-rpi-3-latest.tar.gz -C /Volumes/ROOT

Now we just expanded everything to root, but the boot stuff needs to be on the BOOT partition. Move it over. You could use mv or be safer with rsync

mv /Volumes/ROOT/boot/* /Volumes/BOOT/

Flush out the kernel buffers to disk.

sync

Unmount and you are good to go.

diskutil unmount /Volumes/{BOOT,ROOT}