Is there any security risk from my kids knowing their minecraft password?
When I created a Minecraft account for my kids, I had to create an account on Mojang and buy a Minecraft account using a credit card.
As my kids use the Mojang account details to sign in to Minecraft, I've been reluctant to allow them to know the password. But they need to keep signing in as it times out the login credentials from time to time and it would be more convenient if they knew their own password.
Are there any security implications from them knowing their own Minecraft passwords? My primary concern is the fact that I used my credit card to buy the original account, but also there may be other implications given that once the kids know them, I don't have the same level of security over the passwords as when only I know them.
Minecraft does not save credit card details, so there is no risk of your kids spending all your money on merchandise or buying more copies of Minecraft.
The only risk I can think of would be if they gave the password to their friends and lost the account that way, but you're the parent here so it's up to you how you stop them doing that.
No, there is no security risk. In fact, Mojang doesn't save credit card data. Once you bought a copy, it won't store it and/or ever use it again.
But to answer your question, no, there is no 'big' security risk.
Theoretically, there is no concern. When you buy Minecraft for an account, the system uses the credit card's info to charge the $27 you spend for the game to your card, and doesn't ever use it again. The only thing a Minecraft password can be used for is to change the player's skin by signing on to Minecraft.net, and logging in on the Minecraft Launcher in order to play.
As others have said, the worst they can do is lose the account; however there are a number of phishing scams out there specific to Minecraft. Make sure you educate your kids about what websites they should log into with their Minecraft account and who they should give the password to. The answers being simply, Minecraft.net, Mojang.com, and no one and nothing else.