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How leprosy was considered in the Middle-Ages is an interesting story, because it evolved quite rapidly at the end of the 12th century, but differently depending on the place, and Baldwin IV was used as example.
If you read French, read this article from Mark Gregory Pegg (it is a translation; I could not find the English original online). As a rough summary:
In the Latin world (Western Europe), the harmony of the society was considered to be somehow the same thing as the harmony of the body of the King. In 1179, the Pope Alexander III was writing (in his letter known as Cor nostrum) that Baldwin IV was scourged by God and thus incapable to be King, since that would endanger the whole kingdom. This follows a gradual evolution: prior to about 1170, leprosy was an illness of the powerful, but afterwards it became commonly associated with the poor, vagrants, criminals and other disruptive elements of the society. Lepers were thus being shunned, but only after 1170 or so; this was formalized in 1179 in Canon Law.
(An important point here is that medicine in Middle-Ages was not precise enough to properly diagnose what is now known as leprosy. Instead, a number of distinct pathologies were susceptible to be described as "leprosy"; but the term really means accusation of leprosy, a kind of social curse which switched targets around 1170, without that evolution being in any way correlated with actual biology. If you had eczema and were poor, in 1150, you were just a poor man with an itch; in 1200 you became a leper.)
In the Kingdom of Jerusalem, the association between the body and the society was not maintained. Society at large did not consider that the King's illness impacted the society, except indirectly by physically incapacitating the King. Thereby, there was no reason for anybody to claim that being a leper prevented Baldwin from being the legitimate heir and receiving the crown. The Order of Saint Lazarus is a testimony to that: it was established in Jerusalem in 1098 by the just-arrived Crusaders, and became a military order at some unclear date during the 12th century. That Order was dedicated to the treatment of lepers. Lepers were thus integrated into the society, considered to be ill, not cursed.
Thus, Baldwin IV could become King of Jerusalem because, indeed, it was in Jerusalem, not in France or Italy. However, the case of Baldwin IV was instrumental in the generalized shunning of "lepers" which went in full swing in the West at the end of the 12th century.