You can't open your inventory by pressing 'E' while inside a nether portal.
MC-152986
can't open inventory in nether portal
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I think this is more of a feature since moving items right before the teleport could lead to them being dropped and you being teleported in another dimension.
If you were to be moving an item when the teleport occurs you would drop it outside the portal (when the inv is forcibly closed) and immediately be teleported to the other dimension.