It's really up to you. I have seen them both ways. The do fairly well to leave the inner seal in place. However the vast majority have thew inner seal removed,

Jim

Bohunk your intuition is correct do your self a favor your bering will love you for it, always remove the inside seal of a front main.

The most likely reason your replacement factory front bering came with a double seal is simply your factory did not make them and did not special order them as a single side seal.

Just an opinion, John

As John says, remove that inner seal but also thoroughly clean out all the pre-packed grease before installing the bearing. That grease isn't designed for the revs our engines run at and the balls could skid which won't do them much good. Personally I'd go for just a shielded bearing (in which case you can leave both shields on). A little oil coming out the front doesn't worry me because then I know the bearing's being lubricated. The flow of oil to the front bearing is controlled by the fit between the front of the crankshaft and the crankcase and usually gives something like .001" clearance. The oil (well, fuel actually) gets forced forwards by the average positive pressure in the crankcase. It seems to me that if you use a sealed bearing, even if only the front seal remains, then it could stop the flow of oil or at least restrict it to the point the bearing doesn't get enough.