Your class and all starting class features, such as skill proficiencies, are chosen before backgrounds — see PHB pages 11–15 for the order of operations. So yes, you can select overlapping skills for your barbarian before taking the Outlander background, then get to choose any two skills instead.

A minor reason you might not want to do this is because the trick locks you into choosing Outlander / not choosing any other background.

I haven't been able to find any authoritative ruling on this anywhere, and the various People on the Internet who were talking about it had multiple different rulings, so I'd expect table variation.

At my table, I would rule that you can take a different skill (via the "if something gives you proficiency in a skill you already have you can pick another" rule that you quoted), but that the expertise would only apply to one of those four skills listed under Blessings of Knowledge (and you'd get it for the skill that you already had), so this isn't some backdoor way to get expertise in some random skill. That feels closest to the Rules as Intended IMO.