OSSS ID Card and Bing Receiver

Are those 2 items needed to do the quests? Because I run out of inventory space quickly, but I don't want to throw away something necessary to enter the base/do the quests.

You need the OSSS ID Card to do Stage 1 quests, and possibly Stage 2 and 3. (No one has tested it yet.)

Not sure about the Bing Receiver.

Receiver can be reobtained infinitely from the bum guy so it's not an issue. Drop it when you have to and get it back later, i've done it several times so far.