Unusual but not incorrect. My understanding has it that the religious sense is a (very common) specialization of a more general meaning along the lines of "treating different groups the same".
No, I think "ecumenical" in the less common sense of the word, "worldwide or general in extent, influence, or application," makes perfect sense here. Or even in the usual sense of the word, if you're making an analogy between startup accelerators and Christian denominations. It's a pretty good analogy, since despite small differences in belief and large differences in culture and practice, everyone has roughly the same goals. A Lutheran might feel particularly slighted at a program that gives free choral music to Anglicans, because they sing all the same anthems and none of the differences are relevant, and so restricting the free stuff to Anglicans rubs in the difference for no good reason. This is quite different from the way a Buddhist or an atheist would feel slighted by not getting that free music.
Given that OP claimed the feeling will pass, I don't think "economical" quite makes sense.