I haven't done the research because I don't feel like scanning hundreds of threads. Can you make a deck with nothing but unaffiliated cards? Or do you have to have a house card?

worldeater said:

"Each player chooses to play one of the six Great
Houses, and this choice is signified by that player’s
House card."

So yeah, you have to have a House card. You're in a heck of a lot of trouble if you don't have one since that's where you accumulate power (that you don't put on characters) and, if you want to play an agenda, you have to have something to attach the agenda to.

Luckily, as shown, the Neutral Faction gives you an option other than the 6 Great Houses. You have 7 choices for House card, but you must have one of those 7 in order to play the game.

Thanks for the information. I am still new to the game and I had never seen the neutral faction card until today. Thanks again for pointing that out for me.