Well, from what we know the minimum of Federation required participation is joined military forces (Bajoran example), shared knowledge and technology (Memory Alpha) and shared resources.
Population is not drafted into Starfleet, there is a clear majority of founder and core member worlds providing voluntary forces..
But existing military has to switch uniforms.
Requirements to join the Federation in the first place are a minimum technological level (warp capable) and social development level.
Global unity is important (Kes-Pritt).
Any member world can provide a presidential candidate, we have seen 2 aliens doing the job.
We know the Federation counsel has a say in overall Starfleet matters but I don't remember the council overruling a particular world goverment (with the possible exception of Earth, which seems to have become the Federation capital in a similar way as Washington DC or Berlin are their nation's capitals without belonging to a single federal state.