Are there any instances where "gegen" and "gegenüber" mean the same thing?
I know of one instance where they can be used more or less interchangably:
"Eine Forderung gegen jemanden haben" is an idiomatic way of saying "to have a claim against someone."
"Eine Forderung gegenüber jemandem haben" is slightly less idiomatic, but still correct German.
But this is just a coincidence: It's the only instance I can think of where "gegen" is the more or less meaningless preposition associated with a noun (rather than, say, a meaningful preposition denoting a direction or something like that), and "gegenüber" can pretty much always stand in as that sort of preposition, especially when the most idiomatic usage is mostly known to professionals.
I should also add that I'm not convinced that they "mean the same thing" here, since they are both more or less meaningless in this context. (Is nothing a thing? Do two things that mean nothing mean the same thing?)