Yes. The live dealer games are safe and secure. The software providers have put in several features to ensure that your personal data is not leaked or hacked by other parties.
First, you play card games on the casino account platform where you are protected by the casino security measures that include encryption and anti-malware systems.
Second, the live dealer does not see all your personal details when you join a table, but only an identifying ID. This means they cannot later use the information out of the table.