The safety issue come in by the fact that once rooted you can do anything to the phone - you can even tell Android (and the Linux OS it's running in) to delete itself - and it will. And you're left with a useless hand warmer. That's why rooting usually voids the warranty - they don't want to have to figure out what you did wrong to cause the problem you're having. (The normal solution, if the warranty were still in effect, would be to reflash the stock ROM - which you can do yourself. Yes, you'll lose anything you haven't backed up to another device, but that's the price of not knowing what you're doing.
Once you understand what rooting is and what it does, you'll see that it's really just the addition of a single file to the phone, which never runs unless some app asks for superuser status, so unless the app asking for it is bad, there's no 'safety' issue.