We have confirmed in the PC version that if you perform any actions while the card animation is playing, you may become unable to select a card and proceed.
For the time being, you can avoid this issue by refraining from pressing anything until the card animation has finished playing. In addition, if you encounter this problem, restarting the game should allow you to proceed.
We are planning to fix this issue in a future update, so please bear with us until then.
We're truly sorry for the inconvenience.