You can still just play the game, nothing has changed. It’s extremely easy to just ignore everything to do with the inventory on Steam, which a lot of people do.

If you don’t want to give Valve and the dev money, you can also trade the cards with other people directly.

You could also recycle certain items into gems and use those to craft booster packs, to eventually get a full set completely by yourself.

Also, the only thing the trading cards are for at this point are the badges, that you can “show off” on your profile. All the other stuff (emoticons or wallpapers) can be bought directly in the Points Shop.