Forgive a layman if this is an ignorant/misled question, I was neither raised in Christian traditions nor am I knowledgeable about the history of Christianity (or feudalism)!
It seems like there a lot of common references to God as a "Lord", or to the "Kingdom of Heaven", or Christians as His subjects, or other such phrases that evoke feudal-ish social and political relations. Did these ideas originate in medieval Europe?
If so, was earlier Christianity informed by pre-medieval political structures? And are there examples of more recent Christian ideas informed by subsequent political structures?
There is no such thing as an ignorant question.
The biblical phrasing of God as "Lord" and the world which he rules over as his kingdom is not a medieval invention.
In Jewish tradition the name of God is YHWH. As you might know the name is taboo for Jews, something that was already the case around the time Jesus lived and later when the gospels and the rest of the New Testament was written.
This taboo lead to other names being used to refer to god, most notably "adonai". When early Christian authors wrote down the gospels they didn't write them in Hebrew or Aramaic though, they used Koine Greek, the lingua franca of the east Mediterranean region at that time. This mean that they didn't use the Hebrew name "adonai" but the Greek "Kyrios", which has already been used as a substitute of YHWH in the Septuagint, the Greek translation of the Jewish Bible. The literal translation for Kyrios into modern English is "Lord" or "Master", even though in ancient times it referred to the head of the family rather than an actual Lord as a noble ruler of sorts.
The same can be said for the Kingdom of God/Kingdom of Heaven. In the Hebrew bible the term used is "malkuth" which is directly derived from maelaekh - the Hebrew word for King. In the Greek translations (and therefore later in the New Testament) they used "basileia", which again was also a common term for earthy rulers and their domains. The emperor of the Byzantine empire was referred to as "basileus" for example.
So yes, the idea of God as a ruler and the world and it's people as his realm and subjects is certainly an image of real world political structures, but it predates medieval times.