The phantom steed spell creates a "Large quasi-real, horselike creature" that can be ridden by "you or a creature you choose". "You decide the creature’s appearance" and it "uses the statistics for a riding horse."
The rules for mounted combat state that "A willing creature that is at least one size larger than you and that has an appropriate anatomy can serve as a mount"
Can a mule ride on a phantom steed?
The conditions appear to be that (1) the Steed is willing (which I think we can assume from the nature of the spell), that (2) it is a size larger than the mule (Mules are Size Medium, Riding Horses are Size Large), and that it (3) has "appropriate anatomy".
Now, obviously a real riding horse does not have an appropriate anatomy to be ridden by a mule.
But the phantom steed is not a riding horse. It is a "horselike creature", whose appearance is decided by the spell's caster.
So, RAW, does anything prevent the caster from stating that the steed created has its appearance including appropriate anatomy to be ridden by a mule, any other size medium or smaller quadruped, or other non-traditional riders?
At the GM's discretion.
The size is appropriate. The willingness is also clear since the spell specifically states that the caster or another designated creature can ride the phantom steed.
The condition of appropriate anatomy is rather vague which may be because it is rather clear what animals / monsters a human(oid) can ride on. It is unclear, however, what the appropriate anatomy is when the mounted combatant is a mule. "Horse-like" and using the Riding Horse stat block indicate that the appearance cannot be completely freely decided.
In the end, however, it is up to the GM to decide how far you can deviate from the standard horse and, more importantly, if "appropriate anatomy to be ridden by a mule" is a sufficient description of the appearance. The GM is clearly within their right to have you describe how the anatomy is appropriate.