I had a question about installing home-brew on the Wii U. I heard it's safe(within reason), but some games say that they will deactivate if unauthorized software is installed. if I install HBC will that make Mario Bros, etc permanently stop working? also after installing is there a way to remove all traces of it or will it always leave a stub in the memory?
It's as safe as any other unauthorized software; user beware. There are no guarantees for perfect safety, nor unlimited usage. It can even brick your system if you do it wrong. Official updates may remove your homebrew or other software, or even brick your system, and you won't have any recourse, since installing unofficial software invalidates your warranty. Anything you do is solely your responsibility.
That said, I have yet to find any sort of bricked Wii whatsoever; the process is pretty painless, and effort has been invested to ensure only stubs are replaced with the custom software. Usually, that same software can bypass the official Wii launcher, so you don't even need to update the system to play them. But take that with a grain of salt, because it's always a cat and mouse game between the console manufacturers and the homebrew scene. Just because it works now does not guarantee it's future functionality or that it will work the same as it does now.
In the homebrew scene, there are no safety nets or guarantees. Use at your own risk.