I did a passenger mission in which a physical reward would be given upon completion, on top of the money. I didn't have a cargo bay, so when I landed at the last stop to let 'em off, there was no option to complete the mission. After some useless googling (in which people were talking about self desctructing just to get the passengers off their ship), I looked in the mission description and noticed that there was a physical reward. When I swapped out a module with a cargo bay, I was then able to complete the mission.
If it's a mission that you can't complete without a cargo bay, you should be required to have the proper sized cargo bay before you accept the mission. Or at least, when you land, the passenger board should say something about you needing the cargo bay, or let you store the cargo at the station if you can't outfit a cargo bay (but honestly, it would be smarter just forcing people to equip a cargo bay before signing up for the mission, in case the station doesn't have outfitting).
If it's a mission that you can't complete without a cargo bay, you should be required to have the proper sized cargo bay before you accept the mission. Or at least, when you land, the passenger board should say something about you needing the cargo bay, or let you store the cargo at the station if you can't outfit a cargo bay (but honestly, it would be smarter just forcing people to equip a cargo bay before signing up for the mission, in case the station doesn't have outfitting).