You can trust Arch. Manjaro and various other distros are based upon, or are derivatives of, Arch. It’s like Ubuntu is based upon Debian. Arch is a big deal. Can you trust companies (Microsoft, Facebook) or governments? Ultimately the setup around the kernel that is Linux is a global community of software developers and software users. If you don’t trust the concept of Linux and it’s ecosystem then…???
In the open source world people want things to work, and most of the development work is done voluntarily by skilled people who rely on donations or sponsors , or by having another job. They have no interest in deceiving you with dodgy software. Of course sometimes the software will break in some way, but it is quickly fixed due to the community commenting upon it. Compare this to the nightmare of big company eg Windows updates that break allsorts of things and then are patched up with more hasty fixes and bad coding. Give me the Free Open Source Software global community (which includes Debian, Arch etc etc) over big corporate companies (who do not care about you and basically exist to make a profit for themselves and the shareholders who invested in them) anyday!