As I understand it, there existed, in general terms, a Greco-Roman view of sexual relationships between men. A generally acceptable homosexual relationship would be one between a more powerful older man, and a younger, less powerful man/adolescent. For example, Hadrian's relationship with Antinous. Being seen as masculine, and in the modern gay lexicon, a top, made this relationship acceptable. Whereas, an unacceptable relationship would be one where one could find their masculinity questioned. For example, when an adolescent Elagabalus takes older more masculine lovers, becoming a feminized 'bottom' in the popular imagination.
Yet, something seems to be changing by the 4th century. In 390, the Salonika riots are started by German auxiliaries arresting a famous charioteer, for having sodomized a male servant. Around the same time, laws are being passed against men taking on a feminine sex role.
What's going on to cause this shift? Obviously, the Empire is Christianizing and Germanizing during this period. Is this the cause for the shift in sexual mores?
Follow up question on Church history, when/how was the book of Leviticus, including its currently famous lines condemning both participants of homosexual sex to death, included in official Roman Christianity?
According to David Halperin ancient Rome did have a gender system that was less divided into male/female but rather penetrator/penetrated. For a free Roman man to have sexual relations to one or several of his male slaves was entirely normal and even expected. However, a male Roman citizen was culturally only allowed to be the one penetrating as you already mentioned. To the point that the immanent danger of a former Roman citizen becoming penetrated was taken as the reason to abolish debt slavery for Roman citizens. According to James Neill the reason for this 'topping only' mentality was the strongly chauvinistic, imperialistic self-image of the Romans. As an ever expanding empire Rome was conquering and ruling other nations, so no Roman man was allowed to let another man "conquer" him. This unspoken rule also helped to keep the (compulsatorily heterosexual) ideal of the Roman male as the "pater familias" (being the father and ruler of his own family like the emperor is father and ruler of Rome) intact while allowing men to have sex before and outside their compulsatory marriage. Interestingly, while female prostitutes were of the lowest social rank in Rome male courtesans were often held in very high regard and could set their prices accordingly.
This system started breaking down when the rising stoic ideal of the abstaining male started clashing with a relaxation of 'same-sex relations only with inferiors'-rule and the failing leadership of the empire after Marc Aurel. This started a nationwide restrengthening of the "pater familias" concept in a way stricter form than it had been ever before in an attempt to rediscover the true Roman spirit. Thus, homosexual behavior fell suddenly very out of favor in the Roman empire.
Sources: "Is There a History of Sexuality?" David M. Halperin, History and Theory, Vol. 28, No. 3 (Oct., 1989), pp. 257-274.
James Neill (2011). "The Origins and Role of Same-Sex Relations in Human Societies"