By far the worst idea? So we don't need lower AE impact? More diplomatic slots so we can have more vassals? Lower cost to annex those vassals? More diplomatic reputation to reduce the time for annexing them? Or a 50% reduction of the cost of unjustified demands? Etc. And the synergy with Religious and our National ideas that allows a 95% reduction in culture conversion cost? Without that synergy it wouldn't be that great, but with it it's outstanding.
Wrong culture provinces give +2 local unrest, -33% local tax and -33% local manpower. Wrong culture and wrong religion gives +6% local unrest, -66% local tax, -33% local manpower (plus the impact the reduced tax has on manpower), -30% goods produced (+tax impact), and the tax impact reduction in trade value... At the best of times those provinces are worth 1/3rd of a right culture/right religion province, at the worst they are a rebel spawning liability with a Local Autonomy that can't be lowered and reduces their value further.
If we pick Influence and Religion we can get rid of those penalties almost for free and if we're going to expand we will have a lot of provinces to convert. The benefits will be enormous. And, yes, Religion is the better idea group. Which is why I argued to pick it instead of Administration. But we will have a lot of diplomatic points by the time we hit the next idea group so a Dip idea is the logical choice. And Influence is the best Diplomatic idea.