From very early on, it is religious in origin. There's a statement ascribed to the prophet Muhammad where he ordered his followers to trim their mustaches and grow their beards. You can find this in the hadith corpus, specifically in the collection of Bukhari and Muslim.

Later Muslim scholars debated whether this statement was a statement of obligation or recommendation. They then further debated whether this meant a prohibition on shaving the beard completely or even trimming it at all. If you're doing this for research, I can give you further reading from the different guilds of Islamic law but in short, the concept of a beard with little to no mustache is indeed religious in origin.