We are considering reducing our loan origination fee if the customer opens a deposit account. Is this allowable?

I can't think of anything preventing it. There's not a problem with anti-tying because it is a traditional banking product.

If you have a large unbanked population that presents a prohibited basis disparity, you may want to make sure that you have your "business necessity" documented for fair lending purposes for the variance in pricing.

On the other hand, if you have well defined products to assist the unbanked, this may encourage them to be "banked" and provide home ownership incentives at the same time.

Fair lending wouldn't be my primary concern, but I would address it.