I believe the only cards you can't sell are random weapon and vehicle cards. Though I wouldn't do so anyway unless you completely avoid Warzone since they often give players primo stuff.
I sell like 75% of the stuff i get, what use do you have of 19 mongooses, or 13 SAW's.
I usually keep somewere between 3 to 5 cards of one weapon or vehicle, the rest i sell.
The random weapon or vehicle cards, I only keep rare and up.
Powerups I also sell seeing as there useless as well.
There is absolutely no reason te keep all your req cards, don't use it, sell it!