This holder is a very easy print without supports.
It's meant to be very easy to clean. The holder itself doesn't get dirty, instead any water drops will just drop onto your tiles and can easily be wiped away.
The heads are not meant to snap in, instead they just drop in. Thanks to their slight taper and their slightly oval shape they even align themself nicely.
Your printer doesn't need to be very accurate.
The two parts need to be glued together.
I recommend printing it with some kind of white filament.
Designed with Fusion 360
The author hasn't provided the model origin yet.