While you are inside a nether portal in survival you are not able to open your inventory. I noticed this bug in the versions 1.15 - 1.16.1. It is a bit annoying because you cannot manage your inventory while you are entering the nether. You can although pause the game and open the debug menu fine. When I tried entering the nether while having my inventory opened, it would automatically close. To do so, I used powered rails and an activator rail to put me in the nether portal (you can see an image of my setup below). Then I hopped into the minecart and open my inventory.