The second option is kind of how I see this. Utopian living conditions and no free movement, no political rights, no tolerance for dissent.
That sounds pretty authoritarian to me.
The way I see it, we have a religion. We take it very seriously. It promotes spiritual enlightenment over earthly concerns. (Fanatic Spiritual)
Either the religion is inclusive of other races, or we simply like to interact with those other races (maybe because we are naturally friendly). (Xenophile)
We are neither particularly authoritarian, neither particularly egalitarian. We don't control peoples lives, but neither are individual rights a given. People can generally do what they want, as long as they don't cause trouble. Places where we crack down might be religion (depending on what our religion is), and probably state security (we are an Imperium). Do we have a god emperor, or do we separate church and state?
We are neither particularly militaristic nor pacifistic. We don't spread our creed through military might (generally), but are ready to defend ourselves, and maybe use war as an extension of politics.
So, of the top of my head,a possible setup is the empire is officially headed by the Great Stem, a psionic shroom of tremendous size that grows on the home world. The feelings of the Great Stem is law. They are generally quite liberal laws, but they have no power in themselves. The Great Stem could overturn them at any time if it wished (which it generally doesn't, but still). The Fungoid don't exactly worship the Great Stem, but are more followers of its philosophy, acknowledging its superior wisdom and enlightenment. Basically a Fungoid form of taoism. The philosophy highlights interpersonal relationships, promoting empathy, trustworthiness and serving the community by respecting your superiors. The hierarchy goes all the way to the Great Stem, so if you trust your superior, and he trusts his, and so on to the top, all will be guided by the Great Stem.
However. A certain amount of evangelising also occurs. Those that do not follow the Great Stem, should be convinced to do so, for their own spiritual enlightenment. It might even be worth forcing them into the fold.
Fungoids aren't genetically predisposed to obeying the Great Stem. Some have their own ideas. Those Fungoid who are able to work towards their own promotion, while mimicking adherence to the path are more likely to rise towards the top, than those that simply serve their fellow Seeds as the path would suggest. The top hierarchy are filled with politically astute fungoid, some which actually believe in the path, and others which just use it for their own ends.
The Great Stem might be a telepathic, building-sized, nigh-immortal being. But it isn't actually that much smarter than the average Fungoid. It has a plan, and it can act over long times to enact those planes, but it can't see the future, and it can't control every corner of the empire. It knows this, and thus has a pretty hands off approach. It passes its thoughts on to the Fungoid, which in turn informs their laws, philosophy and culture, but in the day to day, the empire is headed by the grand administrator, a life-time appointment. He has direct access to the Great Stem, and often work to pass its thoughts into law, as well as handle the daily working of the state.