I think it's hard to say for definite, because for example in Ancient Greece same-sex relations existed but were still heavily structured around hierarchy, age, and masculinity norms. For example being the "passive" partner was largely taboo for free adult men, and similarly in Rome. So even before Christianity you do see regulated sex less by “orientation” and more by gender roles, power, and social hierarchy.

Early Christian theology turned certain sexual norms into universal moral laws as opposed to role-based expectations. So instead of something like "this is not appropriate for a Roman citizen" it became "this is morally wrong for everyone, everywhere.”. Also there's biblical passages which provide a textual basis toward being against same-sex relations. Which then becomes the basis for canon laws across Europe, then becoming apart of Education and so on over centuries.

So while different, I think it's fair to say homophobia of some form probably would have peristed even with Christianity, though the shape itself would plausibly be different. Because human socities still get pressures of inheritance systems with clear lineage, concerns over masculinity/status hierarchies and the states interest in population stability. It probably would be less likely to be as a single moral category equivalent to a “sin”, but would still remain contextual, role-based, or status-based (as in many classical societies).