In some cases there were Antipopes - that is, a rival claiming to be the true pope. Of course, each declared the other to be the Antipope! This was the case during Roger II of Sicily's disagreements with the papacy. In Roger's case the hostilities were usually initiated by the pope rather than the king, which might have helped. Regardless, one of the greatest disputes Roger had with the papacy revolved around the new Pope Innocent II's refusal to acknowledge him as king of Sicily, and the equally new Pope Anacletus II's promise to support him if Roger returned the favour. At this point, Roger was one of the most powerful rulers in Italy and his backing would be invaluable to Anacletus. Roger, for his part, wanted simply to have his newly assembled kingdom recognised as such, and the anti-Norman Innocent II had no intention of doing so (Houben, Roger II: a Ruler between East and West). In this type of case, both sides have an equal claim to righteous conviction.

As might be expected, a papal schism is not the norm when disputes between secular rulers and the papacy arise, but I think these unusual cases serve as illustrations of a more broadly applicable principle - that clergy, including even popes, can be considered illegitimate. The claim of a pope to divine correctness isn't necessarily swallowed without question. Any pope could be painted as a fraudulent pope. Remember also that God's will is in action. If a ruler goes against the pope and wins, then it was God's will all along and the pope was being ungodly.

Indeed, Helene Wieruszowski argues (in a 1963 article that makes some very valid points despite its age) that the widespread support of Sicily's social elites, magnates and so forth could be taken as evidence that God was speaking through the actions of these powerful citizens - who, naturally, had themselves risen to prominence on the back of God's good will (Wieruszowski, 'Roger II of Sicily, Rex-Tyrannus, in Twelfth-Century Political Thought', Speculum 38:1). Near-universal acclaim by the divinely appointed influential elites is a ringing endorsement of the king's legitimacy and a condemnation of the pope's ungodly error.

To further muddy the waters, the pope was also ruler of a material realm in his own right, and could muster armies and negotiate treaties like any other ruler. The 1156 Treaty of Benevento between Pope Adrian IV and William I of Sicily is an interesting example. Although the concessions that it requires from Pope Adrian are ecclesiastical - that is, it demands papal recognition of the Hauteville kingdom of Sicily in perpetuity - in most respects it is like any other treaty between two rulers. (ed. Enzensberger, Guillelmi I Regis Diplomata and, for an English translation, ed. Loud, The History of the Tyrants of Sicily by 'Hugo Falcandus' 1154-69). Clearly the popes were treated as susceptible to mundane negotiation like anyone else.

My point here is there's evidence that popes weren't thought to be unassailable and so defying them wasn't necessarily as unthinkable as we might imagine.

Of course, the best we can do here is to speculate based on limited evidence. There's very little record of what an 'average' citizen, soldier or otherwise, thought about anything during the middle ages. They didn't govern and they weren't literate, so couldn't write their own letters or diaries. The lesser nobility who followed the kings most likely did so out of self interest, which brings me to my final point.

I want to throw in a thought that one of my undergraduate professors always reminded us of: people are always people. In the present day, many of us would be more likely to follow our immediate ruler over a lofty figure from hundreds or thousands of miles away, someone who is more an abstract idea than a tangible, real person. If we stand to gain (or simply to avoid hardship) by following our king or government to war against a faceless abstract concept who we have never seen and who doesn't even know we exist, many of us will go with the tangible, the things that are real to us. People are always people; follow your king against your pope because he's here and his best interests probably overlap with your own.