Two opposite phase circuits in one conduit... do i need 2 neutrals or an oversized neutral?

Im running two individual single pole 20A circuits though a single 1/2" EMT conduit and hanging a duplex outlet every 6′. They will alternate which circuit (phase) is feeding them (im running black and red 12AWG for these to simplify hook up) Ive also got 2x 12 AWG White neutrals… and everything gets grounded through the metal conduit.
Do I need both neutrals (the sketch shows a common neutral)?
And if I can run a single neutral do I need to upsize it from 12guage?

Update:
I ended up running an additional neutral because all of the outlets needed to be GFCI protected. The First box on the string contained two GFCI outlets, each with separate neutrals and a different hot leg. The following string had one outlet from each GFCI LOAD side (also with labled paired neutrals) Here is the final outlet in the string (the lower 120V one with 2 duplex 120s) we kept the two phases on different color outlets (white and tan) but used a DUAL Pole 20A breaker with handle tie, so that when we shut off the box, both circuits were cut. (The Top outlet, NEMA 6-50 is on its own branch circuit in its own conduit).
The the shop now has Three of these 120V utility branch runs, with 2 independent hot and neutrals handle tied in three 20A 2pole breakers ( plus another 3 50A 2poles for the 240v circuits!).