I talk about the principle. You talk about outcomes. In principle, the society was organized around voluntary exchange of goods and labor for military protection, which is vassalage. The outcomes rarely demonstrated fluidity of vassal-lord relationship because in general trade and movement was restricted, and because the nature of loyalty is such that it is a coin of value only if changed extremely rarely.
The back and forth nature of the chaotic church/government relations of that time only demonstrates that their were super states, that the church from time to time was the super state, that the church at other times was nothing more than a vassal to a non church super state
It demonstrates that the state and the church were orthogonal structures of power that coexisted in tension.
select the best century
West Europe, 400 - 1400, take your pick. The early Middle Ages (till 11 century) had a better pronounced anarchistic system of self-government and voluntary vassalage. In the High Middle Ages (11 - 15 centuries) monarchies began to appear, offset in power by a more centralized and politically assertive church. Quality of life and fecundity of culture were markedly better past 10 century.
The principle you present here never existed to even be considered. The few places where it was put into actual practice, it happened only for a very short time (never more than a half century). Vassals as such did not even make a widely accepted appearance until the 11th century, and they did not relate much to common people until the 13th century. There was no established set of rules or written set of principles, on which guidance could be found for governing society, except possibly the mild punitive measures that could be enforced against the unwarranted killing of slaves, as set out by the Council of Worms in 876. But it would be several hundred years before that restriction was common place in Europe.
As Europe moved into the more modern Monarchist Era in the 13th century, new laws came into being and became common place for cutting off legal escape into the church as well as freeing military service, and thereby common people became increasingly locked in to their involuntary status as either slaves or serfs. The only voluntary options open to the common people, at that time, was the common practice among the few freemen and freedmen to volunteer to become slaves or serfs so as to avoid starvation. That of course was limited to the few of them who lasted long enough without breaking one of the many many local laws that resulted in their enslavement before hand.
...the state and the church were orthogonal structures of power that coexisted in tension.
Actually, this could be more accurately stated that secular powers and the church powers were orthogonal structures... But I would not agree, except to say that only occasionally was this true. For the most part the church was a super state governing over its various areas to varying degrees. In some situations, places, and times, the church was weaker than the secular powers, while in others it was stronger. Over all, every century between the 400 and 1400 was so all chaotic, that it is impossible to say which was more so.