I down voted the other responder. Because Trump is using public key to encrypt the message. You can share your public key as much as you want and people will be able to send you messages that only you(owner of private key) can decrypt. There is no problem. That is normal use of public key to send encrypted messages to the owner of private key.

You can do it also the other way around, encrypt data with private key and only people who have your public key will be able to decrypt it. Which is a bit less useful but it can confirm your identity. So they can be sure that you sent the message.