Yes, Magisk Manager is a safe application; you have nothing to worry about if you use your head and some common sense. Having said that, it is not a tool that can be recommended to anyone who does not have a minimum knowledge in the field, because if you do not use it correctly, this could lead to severe problems, such as the terminal being bricked, which basically means that the device is rendered unusable forever.
As an application or APK file, it is a totally secure tool. The app delivers exactly what it promises and does not host any kind of malware or other security issues. After running it through dozens of antivirus programs, we can say that it is entirely safe in terms of IT security.
In terms of operation, you should know that using Magisk Manager means that you have to have a rooted phone. Rooting a phone involves some additional risks in terms of security, hence the importance of knowing exactly what you are doing. A modification in the rooted operating system, especially in critical areas, could, in a worst-case scenario, render your smartphone or tablet unusable. This is why it so important that you carry out some thorough research before performing sensitive operations.
In any case, these security problems do not go beyond the usual issues when a user roots a phone. Magisk Manager will enable you to hide from other apps that your phone is rooted, which is its primary task, while you remain safe without any security issues.