Ralph, it is permissible when finishing an end grain cut to feed in the opposite direction making sure if it's on the table to hold the wood firmly and have a starting pin or the fence to guide the wood into the cutter. If hand held the wood must be firmly clamped, I don't recommend so called router mats for this operation, and the router must be held firmly.
What George said about routing the end grain first is important and applies to all projects.
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