Yes, it is now indeed possible to share selected cards in Stocard via text message, email or various other messaging or social media apps. You can of course always also restore a full backup of your card list in Stocard on someone else's device. However, if your would only like to share selected cards, the new card sharing feature might be more suitable.
All cards that can be shared now either have a "Share Card" button below the barcode (iOS) or you can open the menu bar (by clicking on the three dots in the upper right corner of your card screen) and choose "Share" (Android).
By sharing a card, you will send a link that enables your friends or family to add your card to their own Stocard app. Please keep in mind though that the link you send expires after a short amount of time and has to be send again if it is not opened in time.