Population really is irrelevant to nation status. There are a ton of very tiny nations throughout the world with tiny land mass (Israel) and tiny population (Luxembourg comes to mind).
Both of which are far larger than the Vatican.
My point is that if you remove the religious aspect from the Vatican, it becomes less relevant and important than my neighborhood, which is roughly equal in area and far larger in population. So yes, recognition of it is a religious thing as it has no importance beyond a religious HQ. And no one recognizes Mount Athos, despite it being in a similar state.
The first line was directed at you. The second part was directed at BRTD. The bit about Mussolini is absurd. Plenty of horrible people have created and run nations. We don't simply refuse to recognize them and hope to wish them away. And of all places, Vatican City is not some place of horrid crimes. It is recognized as an independent state, so what does it really mean to deny its existence?
What you refer to is a very common practice. Plenty of countries including the US refuse to call Burma by the name the junta calls it (Myanmar). Liechtenstein won't even recognize the Czech Republic and Slovakia because of a land ownership dispute.